Development ofAlgorithmic Constructions

 06:40:28 29.Feb 2024

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 odd number < 2000 :
 0 + i ^2 0 + i02+12 = 1 ^2 0 + i02+12 = 1 1 + i12+12 = 2 ^2 0 + i02+12 = 1 (13,7)* (0)=(7) (-7,13)  (1)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + i12+12 = 2 (24,13)* (1)=(6) (-13,24)  (1)=(11)32 + 42 = 52 3*5-1=13, 4*5-1=7 4 + 5i42+52 = 10 3 + 4i32+42 = 25 11 + 15i112+152 = 5 3 + 10i32+102 = 16 1 + 7i12+72 = 19 2 + 13i22+132 = 18 7 + 13i72+132 = 1 (13,24)* (7)=(0) (-24,13)  (13)=(1)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + 9i12+92 = 20 5 + 14i52+142 = 4 6 + 11i62+112 = 2 (24,18)* (6)=(1) (-18,24)  (11)=(1)32 + 42 = 52 3*5-1=13, 4*5-1=7 ^2 0 + i02+12 = 1 (11,2)* (0)=(2) (-2,11)  (1)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(13,7)* (0)=(7) (-7,13)  (1)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + i12+12 = 2 (11,29)* (1)=(9) (-29,11)  (1)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20(24,13)* (1)=(6) (-13,24)  (1)=(11)32 + 42 = 52 3*5-1=13, 4*5-1=7 3 + 4i32+42 = 25 (26,21)* (3)=(7) (-21,26)  (4)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26 4 + 5i42+52 = 10 (20,29)* (4)=(8) (-29,20)  (5)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20(5,21)* (4)=(1) (-21,5)  (5)=(3)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 7i12+72 = 19 (20,2)* (1)=(3) (-2,20)  (7)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20(10,26)* (1)=(6) (-26,10)  (7)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 10i32+102 = 16 (26,21)* (3)=(9) (-21,26)  (10)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26(29,20)* (3)=(8) (-20,29)  (10)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 6 + 11i62+112 = 2 (24,18)* (6)=(1) (-18,24)  (11)=(1)32 + 42 = 52 3*5-1=13, 4*5-1=7(21,26)* (6)=(9) (-26,21)  (11)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 7 + 13i72+132 = 1 (13,24)* (7)=(0) (-24,13)  (13)=(1)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,11)* (7)=(2) (-11,2)  (13)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20 11 + 15i112+152 = 5 (2,11)* (11)=(1) (-11,2)  (15)=(2)52 + 122 = 132 5*13-1=29, 12*13-1=20 2 + 13i22+132 = 18 (21,5)* (2)=(14) (-5,21)  (13)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 9i12+92 = 20 (21,26)* (1)=(7) (-26,21)  (9)=(8)152 + 82 = 172 15*17-1=10, 8*17-1=26 5 + 14i52+142 = 4 (20,29)* (5)=(10) (-29,20)  (14)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(21,26)* (5)=(4) (-26,21)  (14)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26 5 + 12i52+122 = 14 7 + 8i72+82 = 20 (21,5)* (7)=(1) (-5,21)  (8)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26 8 + 15i82+152 = 10 (20,2)* (8)=(4) (-2,20)  (15)=(5)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,27)* (8)=(1) (-27,27)  (15)=(3)72 + 242 = 252 7*25-1=4, 24*25-1=27 1 + 3i12+32 = 10 (27,4)* (1)=(8) (-4,27)  (3)=(15)72 + 242 = 252 7*25-1=4, 24*25-1=27(5,10)* (1)=(4) (-10,5)  (3)=(5)152 + 82 = 172 15*17-1=10, 8*17-1=26 9 + 11i92+112 = 16 (27,4)* (9)=(8) (-4,27)  (11)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27(26,10)* (9)=(3) (-10,26)  (11)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 2i12+22 = 5 (2,20)* (1)=(11) (-20,2)  (2)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 8 + 13i82+132 = 16 (27,27)* (8)=(9) (-27,27)  (13)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27(29,11)* (8)=(3) (-11,29)  (13)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20 7 + 10i72+102 = 25 (26,10)* (7)=(3) (-10,26)  (10)=(4)152 + 82 = 172 15*17-1=10, 8*17-1=26 10 + 11i102+112 = 4 (27,4)* (10)=(4) (-4,27)  (11)=(9)72 + 242 = 252 7*25-1=4, 24*25-1=27(20,2)* (10)=(5) (-2,20)  (11)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 4 + 9i42+92 = 4 (27,27)* (4)=(10) (-27,27)  (9)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27(21,5)* (4)=(5) (-5,21)  (9)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 15i12+152 = 9 14 + 15i142+152 = 18 (21,26)* (14)=(2) (-26,21)  (15)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 11 + 14i112+142 = 7 (4,4)* (11)=(7) (-4,4)  (14)=(12)72 + 242 = 252 7*25-1=4, 24*25-1=27 7 + 12i72+122 = 7 (4,27)* (7)=(11) (-27,4)  (12)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27 2 + 11i22+112 = 1 (11,29)* (2)=(0) (-29,11)  (11)=(1)52 + 122 = 132 5*13-1=29, 12*13-1=20(2,20)* (2)=(7) (-20,2)  (11)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 3 + 14i32+142 = 19 (20,29)* (3)=(1) (-29,20)  (14)=(7)52 + 122 = 132 5*13-1=29, 12*13-1=20(4,4)* (3)=(6) (-4,4)  (14)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27 6 + 13i62+132 = 19 (10,5)* (6)=(1) (-5,10)  (13)=(7)152 + 82 = 172 15*17-1=10, 8*17-1=26(4,27)* (6)=(3) (-27,4)  (13)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27 9 + 13i92+132 = 2 (11,2)* (9)=(1) (-2,11)  (13)=(1)52 + 122 = 132 5*13-1=29, 12*13-1=20(21,5)* (9)=(6) (-5,21)  (13)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 10i12+102 = 8 (13,24)* (1)=(5) (-24,13)  (10)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 5 + 13i52+132 = 8 (13,7)* (5)=(1) (-7,13)  (13)=(10)32 + 42 = 52 3*5-1=13, 4*5-1=7 ^2 0 + i02+12 = 1 (10,5)* (0)=(5) (-5,10)  (1)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,2)* (0)=(2) (-2,11)  (1)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(13,7)* (0)=(7) (-7,13)  (1)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + i12+12 = 2 (24,13)* (1)=(6) (-13,24)  (1)=(11)32 + 42 = 52 3*5-1=13, 4*5-1=7(11,29)* (1)=(9) (-29,11)  (1)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20(10,26)* (1)=(5) (-26,10)  (1)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 4i32+42 = 25 (26,21)* (3)=(7) (-21,26)  (4)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,2)* (3)=(6) (-2,20)  (4)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20 4 + 5i42+52 = 10 (5,21)* (4)=(1) (-21,5)  (5)=(3)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,29)* (4)=(8) (-29,20)  (5)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 1 + 7i12+72 = 19 (10,26)* (1)=(6) (-26,10)  (7)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,2)* (1)=(3) (-2,20)  (7)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 6 + 8i62+82 = 7 (2,11)* (6)=(7) (-11,2)  (8)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20(21,5)* (6)=(11) (-5,21)  (8)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 9i12+92 = 20 (5,10)* (1)=(2) (-10,5)  (9)=(4)152 + 82 = 172 15*17-1=10, 8*17-1=26(21,26)* (1)=(7) (-26,21)  (9)=(8)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 10i32+102 = 16 (26,21)* (3)=(9) (-21,26)  (10)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26(29,20)* (3)=(8) (-20,29)  (10)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 8 + 10i82+102 = 9 (5,21)* (8)=(2) (-21,5)  (10)=(6)152 + 82 = 172 15*17-1=10, 8*17-1=26(21,5)* (8)=(1) (-5,21)  (10)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 6 + 11i62+112 = 2 (24,18)* (6)=(1) (-18,24)  (11)=(1)32 + 42 = 52 3*5-1=13, 4*5-1=7(21,26)* (6)=(9) (-26,21)  (11)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,29)* (6)=(5) (-29,20)  (11)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 9 + 12i92+122 = 8 (20,29)* (9)=(1) (-29,20)  (12)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20(29,20)* (9)=(5) (-20,29)  (12)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 2 + 13i22+132 = 18 (20,2)* (2)=(4) (-2,20)  (13)=(8)52 + 122 = 132 5*13-1=29, 12*13-1=20(21,5)* (2)=(14) (-5,21)  (13)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 7 + 13i72+132 = 1 (13,24)* (7)=(0) (-24,13)  (13)=(1)32 + 42 = 52 3*5-1=13, 4*5-1=7(10,26)* (7)=(5) (-26,10)  (13)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26(2,11)* (7)=(2) (-11,2)  (13)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20 2 + 14i22+142 = 14 (2,11)* (2)=(3) (-11,2)  (14)=(6)52 + 122 = 132 5*13-1=29, 12*13-1=20(26,21)* (2)=(5) (-21,26)  (14)=(12)152 + 82 = 172 15*17-1=10, 8*17-1=26 5 + 14i52+142 = 4 (21,26)* (5)=(4) (-26,21)  (14)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,29)* (5)=(10) (-29,20)  (14)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20 11 + 15i112+152 = 5 (2,11)* (11)=(1) (-11,2)  (15)=(2)52 + 122 = 132 5*13-1=29, 12*13-1=20(20,29)* (11)=(4) (-29,20)  (15)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20 12 + 15i122+152 = 28 (5,21)* (12)=(3) (-21,5)  (15)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(26,21)* (12)=(7) (-21,26)  (15)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 2i12+22 = 5 (18,24)* (1)=(4) (-24,18)  (2)=(12)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,20)* (1)=(11) (-20,2)  (2)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 1 + 3i12+32 = 10 (5,10)* (1)=(4) (-10,5)  (3)=(5)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,4)* (1)=(8) (-4,27)  (3)=(15)72 + 242 = 252 7*25-1=4, 24*25-1=27 9 + 11i92+112 = 16 (26,10)* (9)=(3) (-10,26)  (11)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,4)* (9)=(8) (-4,27)  (11)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27 4 + 12i42+122 = 5 (18,7)* (4)=(1) (-7,18)  (12)=(2)32 + 42 = 52 3*5-1=13, 4*5-1=7(20,2)* (4)=(11) (-2,20)  (12)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 8 + 13i82+132 = 16 (29,11)* (8)=(3) (-11,29)  (13)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,27)* (8)=(9) (-27,27)  (13)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27 8 + 15i82+152 = 10 (27,27)* (8)=(1) (-27,27)  (15)=(3)72 + 242 = 252 7*25-1=4, 24*25-1=27(20,2)* (8)=(4) (-2,20)  (15)=(5)52 + 122 = 132 5*13-1=29, 12*13-1=20 2 + 4i22+42 = 20 (24,13)* (2)=(7) (-13,24)  (4)=(8)32 + 42 = 52 3*5-1=13, 4*5-1=7(5,21)* (2)=(1) (-21,5)  (4)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 6i32+62 = 14 (4,4)* (3)=(5) (-4,4)  (6)=(12)72 + 242 = 252 7*25-1=4, 24*25-1=27(2,20)* (3)=(2) (-20,2)  (6)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 7 + 8i72+82 = 20 (24,18)* (7)=(2) (-18,24)  (8)=(4)32 + 42 = 52 3*5-1=13, 4*5-1=7(21,5)* (7)=(1) (-5,21)  (8)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 9i32+92 = 28 (13,24)* (3)=(7) (-24,13)  (9)=(14)32 + 42 = 52 3*5-1=13, 4*5-1=7(5,10)* (3)=(12) (-10,5)  (9)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 5 + 12i52+122 = 14 (4,27)* (5)=(3) (-27,4)  (12)=(6)72 + 242 = 252 7*25-1=4, 24*25-1=27(26,10)* (5)=(2) (-10,26)  (12)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26 7 + 14i72+142 = 28 (13,7)* (7)=(3) (-7,13)  (14)=(9)32 + 42 = 52 3*5-1=13, 4*5-1=7(26,10)* (7)=(12) (-10,26)  (14)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 2 + 6i22+62 = 9 (5,10)* (2)=(8) (-10,5)  (6)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26(24,18)* (2)=(1) (-18,24)  (6)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 4 + 8i42+82 = 18 (20,29)* (4)=(2) (-29,20)  (8)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,27)* (4)=(14) (-27,27)  (8)=(15)72 + 242 = 252 7*25-1=4, 24*25-1=27 1 + 15i12+152 = 9 (24,13)* (1)=(2) (-13,24)  (15)=(6)32 + 42 = 52 3*5-1=13, 4*5-1=7(21,26)* (1)=(8) (-26,21)  (15)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26 14 + 15i142+152 = 18 (27,4)* (14)=(4) (-4,27)  (15)=(8)72 + 242 = 252 7*25-1=4, 24*25-1=27(21,26)* (14)=(2) (-26,21)  (15)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 4 + 9i42+92 = 4 (27,27)* (4)=(10) (-27,27)  (9)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27(21,5)* (4)=(5) (-5,21)  (9)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26 10 + 11i102+112 = 4 (27,4)* (10)=(4) (-4,27)  (11)=(9)72 + 242 = 252 7*25-1=4, 24*25-1=27(20,2)* (10)=(5) (-2,20)  (11)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 1 + 10i12+102 = 8 (20,2)* (1)=(9) (-2,20)  (10)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20(13,24)* (1)=(5) (-24,13)  (10)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 5 + 13i52+132 = 8 (13,7)* (5)=(1) (-7,13)  (13)=(10)32 + 42 = 52 3*5-1=13, 4*5-1=7(29,11)* (5)=(9) (-11,29)  (13)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20 5 + 10i52+102 = 1 (10,26)* (5)=(0) (-26,10)  (10)=(1)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,27)* (5)=(2) (-27,27)  (10)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27(10,5)* (5)=(7) (-5,10)  (10)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 2 + 11i22+112 = 1 (11,29)* (2)=(0) (-29,11)  (11)=(1)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,4)* (2)=(5) (-4,27)  (11)=(10)72 + 242 = 252 7*25-1=4, 24*25-1=27(2,20)* (2)=(7) (-20,2)  (11)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 7 + 10i72+102 = 25 (26,10)* (7)=(3) (-10,26)  (10)=(4)152 + 82 = 172 15*17-1=10, 8*17-1=26(4,4)* (7)=(6) (-4,4)  (10)=(12)72 + 242 = 252 7*25-1=4, 24*25-1=27 6 + 12i62+122 = 25 (20,29)* (6)=(3) (-29,20)  (12)=(4)52 + 122 = 132 5*13-1=29, 12*13-1=20(4,27)* (6)=(7) (-27,4)  (12)=(10)72 + 242 = 252 7*25-1=4, 24*25-1=27 7 + 12i72+122 = 7 (2,20)* (7)=(6) (-20,2)  (12)=(8)52 + 122 = 132 5*13-1=29, 12*13-1=20(4,27)* (7)=(11) (-27,4)  (12)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27 11 + 14i112+142 = 7 (21,26)* (11)=(6) (-26,21)  (14)=(8)152 + 82 = 172 15*17-1=10, 8*17-1=26(4,4)* (11)=(7) (-4,4)  (14)=(12)72 + 242 = 252 7*25-1=4, 24*25-1=27 6 + 13i62+132 = 19 (10,5)* (6)=(1) (-5,10)  (13)=(7)152 + 82 = 172 15*17-1=10, 8*17-1=26(4,27)* (6)=(3) (-27,4)  (13)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27 3 + 14i32+142 = 19 (20,29)* (3)=(1) (-29,20)  (14)=(7)52 + 122 = 132 5*13-1=29, 12*13-1=20(4,4)* (3)=(6) (-4,4)  (14)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27 9 + 13i92+132 = 2 (11,2)* (9)=(1) (-2,11)  (13)=(1)52 + 122 = 132 5*13-1=29, 12*13-1=20(21,5)* (9)=(6) (-5,21)  (13)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,27)* (9)=(5) (-27,27)  (13)=(15)72 + 242 = 252 7*25-1=4, 24*25-1=27 5 + 15i52+152 = 2 (10,5)* (5)=(1) (-5,10)  (15)=(1)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,2)* (5)=(6) (-2,20)  (15)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,4)* (5)=(9) (-4,27)  (15)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27 2 + 3i22+32 = 13 (10,26)* (2)=(5) (-26,10)  (3)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,4)* (2)=(4) (-4,27)  (3)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27(2,11)* (2)=(6) (-11,2)  (3)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 4 + 11i42+112 = 13 (27,27)* (4)=(2) (-27,27)  (11)=(3)72 + 242 = 252 7*25-1=4, 24*25-1=27(2,11)* (4)=(5) (-11,2)  (11)=(9)52 + 122 = 132 5*13-1=29, 12*13-1=20(5,10)* (4)=(6) (-10,5)  (11)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 5 + 7i52+72 = 12 (29,20)* (5)=(6) (-20,29)  (7)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,4)* (5)=(8) (-4,27)  (7)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27(7,13)* (5)=(2) (-13,7)  (7)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 8 + 14i82+142 = 12 (27,27)* (8)=(5) (-27,27)  (14)=(7)72 + 242 = 252 7*25-1=4, 24*25-1=27(26,21)* (8)=(6) (-21,26)  (14)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26(24,13)* (8)=(2) (-13,24)  (14)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + 4i12+42 = 17 (29,11)* (1)=(11) (-11,29)  (4)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20(13,7)* (1)=(10) (-7,13)  (4)=(14)32 + 42 = 52 3*5-1=13, 4*5-1=7(11,29)* (1)=(3) (-29,11)  (4)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 11 + 12i112+122 = 17 (29,20)* (11)=(1) (-20,29)  (12)=(4)52 + 122 = 132 5*13-1=29, 12*13-1=20(20,29)* (11)=(10) (-29,20)  (12)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20(18,7)* (11)=(3) (-7,18)  (12)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + 6i12+62 = 6 (29,11)* (1)=(2) (-11,29)  (6)=(8)52 + 122 = 132 5*13-1=29, 12*13-1=20(5,21)* (1)=(7) (-21,5)  (6)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,27)* (1)=(3) (-27,27)  (6)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27 4 + 7i42+72 = 3 (26,21)* (4)=(3) (-21,26)  (7)=(5)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,2)* (4)=(1) (-2,20)  (7)=(8)52 + 122 = 132 5*13-1=29, 12*13-1=20(5,21)* (4)=(12) (-21,5)  (7)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 2 + 9i22+92 = 23 (10,26)* (2)=(6) (-26,10)  (9)=(7)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,29)* (2)=(4) (-29,11)  (9)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20(4,27)* (2)=(3) (-27,4)  (9)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27 2 + 10i22+102 = 11 (5,21)* (2)=(3) (-21,5)  (10)=(8)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,2)* (2)=(11) (-2,11)  (10)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,4)* (2)=(1) (-4,27)  (10)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27 3 + 11i32+112 = 6 (27,4)* (3)=(1) (-4,27)  (11)=(6)72 + 242 = 252 7*25-1=4, 24*25-1=27(26,10)* (3)=(2) (-10,26)  (11)=(8)152 + 82 = 172 15*17-1=10, 8*17-1=26(20,29)* (3)=(7) (-29,20)  (11)=(9)52 + 122 = 132 5*13-1=29, 12*13-1=20 3 + 13i32+132 = 23 (29,20)* (3)=(6) (-20,29)  (13)=(7)52 + 122 = 132 5*13-1=29, 12*13-1=20(4,4)* (3)=(2) (-4,4)  (13)=(9)72 + 242 = 252 7*25-1=4, 24*25-1=27(21,5)* (3)=(4) (-5,21)  (13)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26 12 + 13i122+132 = 3 (13,24)* (12)=(3) (-24,13)  (13)=(5)32 + 42 = 52 3*5-1=13, 4*5-1=7(5,10)* (12)=(4) (-10,5)  (13)=(7)152 + 82 = 172 15*17-1=10, 8*17-1=26(18,24)* (12)=(1) (-24,18)  (13)=(8)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + 14i12+142 = 11 (2,20)* (1)=(3) (-20,2)  (14)=(8)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,27)* (1)=(2) (-27,27)  (14)=(10)72 + 242 = 252 7*25-1=4, 24*25-1=27(26,10)* (1)=(11) (-10,26)  (14)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 10 + 14i102+142 = 17 (13,24)* (10)=(1) (-24,13)  (14)=(4)32 + 42 = 52 3*5-1=13, 4*5-1=7(20,2)* (10)=(11) (-2,20)  (14)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20(5,21)* (10)=(3) (-21,5)  (14)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 15i32+152 = 17 (11,2)* (3)=(1) (-2,11)  (15)=(4)52 + 122 = 132 5*13-1=29, 12*13-1=20(18,24)* (3)=(11) (-24,18)  (15)=(12)32 + 42 = 52 3*5-1=13, 4*5-1=7(5,10)* (3)=(10) (-10,5)  (15)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 7i32+72 = 27 (21,5)* (3)=(5) (-5,21)  (7)=(8)152 + 82 = 172 15*17-1=10, 8*17-1=26(18,7)* (3)=(10) (-7,18)  (7)=(12)32 + 42 = 52 3*5-1=13, 4*5-1=7(29,11)* (3)=(9) (-11,29)  (7)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 9 + 15i92+152 = 27 (29,20)* (9)=(3) (-20,29)  (15)=(7)52 + 122 = 132 5*13-1=29, 12*13-1=20(13,7)* (9)=(5) (-7,13)  (15)=(8)32 + 42 = 52 3*5-1=13, 4*5-1=7(10,5)* (9)=(10) (-5,10)  (15)=(12)152 + 82 = 172 15*17-1=10, 8*17-1=26 2 + 8i22+82 = 6 (29,20)* (2)=(1) (-20,29)  (8)=(6)52 + 122 = 132 5*13-1=29, 12*13-1=20(4,27)* (2)=(7) (-27,4)  (8)=(9)72 + 242 = 252 7*25-1=4, 24*25-1=27(26,21)* (2)=(3) (-21,26)  (8)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26 3 + 8i32+82 = 11 (5,10)* (3)=(2) (-10,5)  (8)=(10)152 + 82 = 172 15*17-1=10, 8*17-1=26(4,27)* (3)=(11) (-27,4)  (8)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27(2,11)* (3)=(1) (-11,2)  (8)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 5 + 9i52+92 = 13 (10,5)* (5)=(2) (-5,10)  (9)=(3)152 + 82 = 172 15*17-1=10, 8*17-1=26(2,20)* (5)=(4) (-20,2)  (9)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,27)* (5)=(6) (-27,27)  (9)=(15)72 + 242 = 252 7*25-1=4, 24*25-1=27 7 + 9i72+92 = 6 (5,10)* (7)=(1) (-10,5)  (9)=(6)152 + 82 = 172 15*17-1=10, 8*17-1=26(4,4)* (7)=(2) (-4,4)  (9)=(8)72 + 242 = 252 7*25-1=4, 24*25-1=27(20,2)* (7)=(3) (-2,20)  (9)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20 6 + 10i62+102 = 12 (29,11)* (6)=(5) (-11,29)  (10)=(7)52 + 122 = 132 5*13-1=29, 12*13-1=20(26,10)* (6)=(8) (-10,26)  (10)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26(29,20)* (6)=(2) (-20,29)  (10)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 9 + 10i92+102 = 26 (13,7)* (9)=(1) (-7,13)  (10)=(5)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,11)* (9)=(4) (-11,2)  (10)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20(7,13)* (9)=(7) (-13,7)  (10)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 8 + 11i82+112 = 30 (18,24)* (8)=(5) (-24,18)  (11)=(6)32 + 42 = 52 3*5-1=13, 4*5-1=7(11,29)* (8)=(4) (-29,11)  (11)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20(29,11)* (8)=(12) (-11,29)  (11)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 11 + 13i112+132 = 11 (4,4)* (11)=(3) (-4,4)  (13)=(8)72 + 242 = 252 7*25-1=4, 24*25-1=27(11,29)* (11)=(2) (-29,11)  (13)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20(26,21)* (11)=(1) (-21,26)  (13)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26 4 + 14i42+142 = 26 (10,26)* (4)=(1) (-26,10)  (14)=(5)152 + 82 = 172 15*17-1=10, 8*17-1=26(2,20)* (4)=(9) (-20,2)  (14)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20(2,11)* (4)=(7) (-11,2)  (14)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 12 + 14i122+142 = 30 (11,2)* (12)=(5) (-2,11)  (14)=(6)52 + 122 = 132 5*13-1=29, 12*13-1=20(29,20)* (12)=(8) (-20,29)  (14)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(18,7)* (12)=(4) (-7,18)  (14)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 13 + 14i132+142 = 24 (24,18)* (13)=(6) (-18,24)  (14)=(9)32 + 42 = 52 3*5-1=13, 4*5-1=7(21,5)* (13)=(2) (-5,21)  (14)=(12)152 + 82 = 172 15*17-1=10, 8*17-1=26(29,11)* (13)=(4) (-11,29)  (14)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 2 + 15i22+152 = 12 (7,18)* (2)=(5) (-18,7)  (15)=(7)32 + 42 = 52 3*5-1=13, 4*5-1=7(29,11)* (2)=(6) (-11,29)  (15)=(10)52 + 122 = 132 5*13-1=29, 12*13-1=20(24,18)* (2)=(8) (-18,24)  (15)=(14)32 + 42 = 52 3*5-1=13, 4*5-1=7 4 + 15i42+152 = 24 (26,10)* (4)=(6) (-10,26)  (15)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(13,7)* (4)=(2) (-7,13)  (15)=(12)32 + 42 = 52 3*5-1=13, 4*5-1=7(29,20)* (4)=(13) (-20,29)  (15)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 6 + 15i62+152 = 13 (2,20)* (6)=(2) (-20,2)  (15)=(3)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,4)* (6)=(5) (-4,27)  (15)=(9)72 + 242 = 252 7*25-1=4, 24*25-1=27(5,21)* (6)=(4) (-21,5)  (15)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26 5 + 8i52+82 = 27 (21,26)* (5)=(3) (-26,21)  (8)=(7)152 + 82 = 172 15*17-1=10, 8*17-1=26(10,26)* (5)=(10) (-26,10)  (8)=(12)152 + 82 = 172 15*17-1=10, 8*17-1=26(13,24)* (5)=(9) (-24,13)  (8)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 10 + 12i102+122 = 27 (18,24)* (10)=(3) (-24,18)  (12)=(7)32 + 42 = 52 3*5-1=13, 4*5-1=7(10,5)* (10)=(5) (-5,10)  (12)=(8)152 + 82 = 172 15*17-1=10, 8*17-1=26(10,26)* (10)=(9) (-26,10)  (12)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 1 + 5i12+52 = 26 (13,24)* (1)=(9) (-24,13)  (5)=(10)32 + 42 = 52 3*5-1=13, 4*5-1=7(10,5)* (1)=(4) (-5,10)  (5)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,27)* (1)=(7) (-27,27)  (5)=(15)72 + 242 = 252 7*25-1=4, 24*25-1=27 7 + 15i72+152 = 26 (27,4)* (7)=(1) (-4,27)  (15)=(5)72 + 242 = 252 7*25-1=4, 24*25-1=27(7,18)* (7)=(9) (-18,7)  (15)=(10)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,20)* (7)=(4) (-20,2)  (15)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 2 + 5i22+52 = 29 (18,24)* (2)=(1) (-24,18)  (5)=(11)32 + 42 = 52 3*5-1=13, 4*5-1=7(29,20)* (2)=(3) (-20,29)  (5)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20(18,7)* (2)=(9) (-7,18)  (5)=(14)32 + 42 = 52 3*5-1=13, 4*5-1=7 3 + 12i32+122 = 29 (29,11)* (3)=(2) (-11,29)  (12)=(5)52 + 122 = 132 5*13-1=29, 12*13-1=20(10,26)* (3)=(1) (-26,10)  (12)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,29)* (3)=(9) (-29,11)  (12)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 1 + 11i12+112 = 29 (18,7)* (1)=(2) (-7,18)  (11)=(5)32 + 42 = 52 3*5-1=13, 4*5-1=7(10,5)* (1)=(3) (-5,10)  (11)=(12)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,4)* (1)=(9) (-4,27)  (11)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27 9 + 14i92+142 = 29 (18,24)* (9)=(2) (-24,18)  (14)=(5)32 + 42 = 52 3*5-1=13, 4*5-1=7(27,27)* (9)=(1) (-27,27)  (14)=(11)72 + 242 = 252 7*25-1=4, 24*25-1=27(11,2)* (9)=(3) (-2,11)  (14)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20 3 + 5i32+52 = 3 (26,10)* (3)=(4) (-10,26)  (5)=(7)152 + 82 = 172 15*17-1=10, 8*17-1=26(4,4)* (3)=(1) (-4,4)  (5)=(8)72 + 242 = 252 7*25-1=4, 24*25-1=27(13,7)* (3)=(12) (-7,13)  (5)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + 8i12+82 = 3 (4,27)* (1)=(3) (-27,4)  (8)=(5)72 + 242 = 252 7*25-1=4, 24*25-1=27(20,29)* (1)=(4) (-29,20)  (8)=(7)52 + 122 = 132 5*13-1=29, 12*13-1=20(18,7)* (1)=(12) (-7,18)  (8)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 6 + 9i62+92 = 24 (5,21)* (6)=(2) (-21,5)  (9)=(12)152 + 82 = 172 15*17-1=10, 8*17-1=26(24,13)* (6)=(13) (-13,24)  (9)=(14)32 + 42 = 52 3*5-1=13, 4*5-1=7(26,21)* (6)=(4) (-21,26)  (9)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 2 + 12i22+122 = 24 (5,10)* (2)=(6) (-10,5)  (12)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(21,26)* (2)=(13) (-26,21)  (12)=(14)152 + 82 = 172 15*17-1=10, 8*17-1=26(13,24)* (2)=(4) (-24,13)  (12)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 4 + 6i42+62 = 21 (10,5)* (4)=(8) (-5,10)  (6)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,29)* (4)=(1) (-29,11)  (6)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20(13,24)* (4)=(10) (-24,13)  (6)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7 8 + 9i82+92 = 21 (10,26)* (8)=(4) (-26,10)  (9)=(6)152 + 82 = 172 15*17-1=10, 8*17-1=26(7,18)* (8)=(1) (-18,7)  (9)=(12)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,20)* (8)=(10) (-20,2)  (9)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 1 + 12i12+122 = 21 (11,2)* (1)=(4) (-2,11)  (12)=(6)52 + 122 = 132 5*13-1=29, 12*13-1=20(7,13)* (1)=(8) (-13,7)  (12)=(9)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,11)* (1)=(10) (-11,2)  (12)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 10 + 13i102+132 = 21 (13,7)* (10)=(4) (-7,13)  (13)=(6)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,11)* (10)=(8) (-11,2)  (13)=(9)52 + 122 = 132 5*13-1=29, 12*13-1=20(2,20)* (10)=(1) (-20,2)  (13)=(12)52 + 122 = 132 5*13-1=29, 12*13-1=20 5 + 6i52+62 = 30 (18,7)* (5)=(8) (-7,18)  (6)=(11)32 + 42 = 52 3*5-1=13, 4*5-1=7(26,10)* (5)=(4) (-10,26)  (6)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,29)* (5)=(12) (-29,11)  (6)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20 4 + 13i42+132 = 30 (26,21)* (4)=(5) (-21,26)  (13)=(6)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,2)* (4)=(8) (-2,11)  (13)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(18,24)* (4)=(12) (-24,18)  (13)=(14)32 + 42 = 52 3*5-1=13, 4*5-1=7 2 + 7i22+72 = 22 (11,2)* (2)=(5) (-2,11)  (7)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(13,24)* (2)=(8) (-24,13)  (7)=(12)32 + 42 = 52 3*5-1=13, 4*5-1=7(13,7)* (2)=(13) (-7,13)  (7)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 5 + 11i52+112 = 22 (11,29)* (5)=(2) (-29,11)  (11)=(7)52 + 122 = 132 5*13-1=29, 12*13-1=20(5,21)* (5)=(8) (-21,5)  (11)=(12)152 + 82 = 172 15*17-1=10, 8*17-1=26(2,20)* (5)=(13) (-20,2)  (11)=(15)52 + 122 = 132 5*13-1=29, 12*13-1=20 8 + 12i82+122 = 22 (13,7)* (8)=(2) (-7,13)  (12)=(7)32 + 42 = 52 3*5-1=13, 4*5-1=7(5,10)* (8)=(5) (-10,5)  (12)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,27)* (8)=(13) (-27,27)  (12)=(15)72 + 242 = 252 7*25-1=4, 24*25-1=27 13 + 15i132+152 = 22 (13,24)* (13)=(2) (-24,13)  (15)=(7)32 + 42 = 52 3*5-1=13, 4*5-1=7(2,11)* (13)=(5) (-11,2)  (15)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,4)* (13)=(8) (-4,27)  (15)=(12)72 + 242 = 252 7*25-1=4, 24*25-1=27 6 + 7i62+72 = 23 (10,5)* (6)=(2) (-5,10)  (7)=(9)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,4)* (6)=(4) (-4,27)  (7)=(10)72 + 242 = 252 7*25-1=4, 24*25-1=27(29,11)* (6)=(3) (-11,29)  (7)=(13)52 + 122 = 132 5*13-1=29, 12*13-1=20 4 + 10i42+102 = 23 (27,27)* (4)=(6) (-27,27)  (10)=(7)72 + 242 = 252 7*25-1=4, 24*25-1=27(11,2)* (4)=(2) (-2,11)  (10)=(9)52 + 122 = 132 5*13-1=29, 12*13-1=20(21,26)* (4)=(3) (-26,21)  (10)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26 7 + 11i72+112 = 15 (10,5)* (7)=(1) (-5,10)  (11)=(13)152 + 82 = 172 15*17-1=10, 8*17-1=26(11,2)* (7)=(6) (-2,11)  (11)=(14)52 + 122 = 132 5*13-1=29, 12*13-1=20(26,21)* (7)=(10) (-21,26)  (11)=(15)152 + 82 = 172 15*17-1=10, 8*17-1=26 10 + 15i102+152 = 15 (26,10)* (10)=(7) (-10,26)  (15)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26(24,13)* (10)=(1) (-13,24)  (15)=(13)32 + 42 = 52 3*5-1=13, 4*5-1=7(18,7)* (10)=(6) (-7,18)  (15)=(14)32 + 42 = 52 3*5-1=13, 4*5-1=7 1 + 13i12+132 = 15 (10,26)* (1)=(7) (-26,10)  (13)=(11)152 + 82 = 172 15*17-1=10, 8*17-1=26(27,27)* (1)=(6) (-27,27)  (13)=(14)72 + 242 = 252 7*25-1=4, 24*25-1=27(24,18)* (1)=(10) (-18,24)  (13)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7 6 + 14i62+142 = 15 (11,29)* (6)=(7) (-29,11)  (14)=(11)52 + 122 = 132 5*13-1=29, 12*13-1=20(27,4)* (6)=(1) (-4,27)  (14)=(13)72 + 242 = 252 7*25-1=4, 24*25-1=27(18,24)* (6)=(10) (-24,18)  (14)=(15)32 + 42 = 52 3*5-1=13, 4*5-1=7

0, 0, ,

All calculation is done with mod f.

The complex number are calculated by exponentation from the botton to the top.

The factorisation depends of the number modulo 4:
Let p be an odd prime, then
for p = 1 mod 4 the factorisation depends on p-1
for p = 3 mod 4 the factorisation depends on p+1

The calculated complex number a+bi depends on the tangens(alpha)= a/b
which describes a rational point on the unit circle.

For symmetric reasons the complex number a+bi is choosen for a < b,
otherwise the tangens(alpha)=a/b is replaced by the cotangens(alpha):=b/a,
that means a+bi:=b+ai for a > b.

If a and b have a common factor with div=gcd (a,b), then a:=a/div and b:=b/div.
(This means that the angle is the same but not the norm (a, b)=a²+b²)

if a=0 then b:=1.

The green elements a+bi are quadratic residues and have jacobi (a²+b², f)=1
The red elements a+bi are non quadratic residues and have jacobi (a²+b², f)=-1
The cyan elements a+bi have a2+b2=0 mod f