Inhaltsverzeichnis

Development of
Algorithmic Constructions

02:27:33
Deutsch
19.Apr 2024

29 31 33
√2 √3 √5 √6 √7 √8

Number p= Adjoined square root=

Calculation

A=√3
(a+bA)² = a²+b²A² + 2abA mod p
|(a+bA)| = (a+bA)(a-bA) = a²-b²A² mod p

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29
Square 2

Number = 31, Adjoined = √3, Exponent = 2, Jacobi (3, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√3
Number of elements = 480

Number = 31, Adjoined = √3, Exponent = 2, Jacobi (3, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29
Square 2

href=2. root

|30+0A|
=1
|30+2A|
=13
|30+3A|
=28
|30+5A|
=14
|30+7A|
=24
|30+11A|
=23
|30+14A|
=0
|30+15A|
=25
|30+16A|
=25
|30+17A|
=0
|30+20A|
=23
|30+24A|
=24
|30+26A|
=14
|30+28A|
=28
|30+29A|
=13
|29+0A|
=4
|29+1A|
=7
|29+3A|
=0
|29+4A|
=21
|29+6A|
=19
|29+9A|
=30
|29+10A|
=25
|29+14A|
=3
|29+17A|
=3
|29+21A|
=25
|29+22A|
=30
|29+25A|
=19
|29+27A|
=21
|29+28A|
=0
|29+30A|
=7
|28+0A|
=9
|28+2A|
=21
|28+6A|
=24
|28+9A|
=4
|28+10A|
=30
|28+11A|
=0
|28+14A|
=8
|28+15A|
=2
|28+16A|
=2
|28+17A|
=8
|28+20A|
=0
|28+21A|
=30
|28+22A|
=4
|28+25A|
=24
|28+29A|
=21
|27+0A|
=16
|27+2A|
=28
|27+3A|
=12
|27+6A|
=0
|27+8A|
=22
|27+11A|
=7
|27+12A|
=14
|27+13A|
=27
|27+18A|
=27
|27+19A|
=14
|27+20A|
=7
|27+23A|
=22
|27+25A|
=0
|27+28A|
=12
|27+29A|
=28
|26+0A|
=25
|26+4A|
=11
|26+6A|
=9
|26+7A|
=17
|26+8A|
=0
|26+10A|
=15
|26+13A|
=5
|26+15A|
=18
|26+16A|
=18
|26+18A|
=5
|26+21A|
=15
|26+23A|
=0
|26+24A|
=17
|26+25A|
=9
|26+27A|
=11
|25+0A|
=5
|25+1A|
=8
|25+3A|
=1
|25+4A|
=22
|25+9A|
=0
|25+11A|
=27
|25+12A|
=3
|25+13A|
=16
|25+18A|
=16
|25+19A|
=3
|25+20A|
=27
|25+22A|
=0
|25+27A|
=22
|25+28A|
=1
|25+30A|
=8
|24+0A|
=18
|24+4A|
=4
|24+5A|
=0
|24+10A|
=8
|24+12A|
=16
|24+13A|
=29
|24+14A|
=17
|24+15A|
=11
|24+16A|
=11
|24+17A|
=17
|24+18A|
=29
|24+19A|
=16
|24+21A|
=8
|24+26A|
=0
|24+27A|
=4
|23+0A|
=2
|23+4A|
=19
|23+5A|
=15
|23+6A|
=17
|23+7A|
=25
|23+9A|
=28
|23+12A|
=0
|23+15A|
=26
|23+16A|
=26
|23+19A|
=0
|23+22A|
=28
|23+24A|
=25
|23+25A|
=17
|23+26A|
=15
|23+27A|
=19
|22+0A|
=19
|22+1A|
=22
|22+2A|
=0
|22+4A|
=5
|22+6A|
=3
|22+11A|
=10
|22+13A|
=30
|22+14A|
=18
|22+17A|
=18
|22+18A|
=30
|22+20A|
=10
|22+25A|
=3
|22+27A|
=5
|22+29A|
=0
|22+30A|
=22
|21+0A|
=7
|21+1A|
=10
|21+5A|
=20
|21+8A|
=13
|21+11A|
=29
|21+12A|
=5
|21+14A|
=6
|21+15A|
=0
|21+16A|
=0
|21+17A|
=6
|21+19A|
=5
|21+20A|
=29
|21+23A|
=13
|21+26A|
=20
|21+30A|
=10
|20+0A|
=28
|20+1A|
=0
|20+2A|
=9
|20+3A|
=24
|20+7A|
=20
|20+9A|
=23
|20+10A|
=18
|20+15A|
=21
|20+16A|
=21
|20+21A|
=18
|20+22A|
=23
|20+24A|
=20
|20+28A|
=24
|20+29A|
=9
|20+30A|
=0
|19+0A|
=20
|19+2A|
=1
|19+5A|
=2
|19+6A|
=4
|19+7A|
=12
|19+8A|
=26
|19+9A|
=15
|19+13A|
=0
|19+18A|
=0
|19+22A|
=15
|19+23A|
=26
|19+24A|
=12
|19+25A|
=4
|19+26A|
=2
|19+29A|
=1
|18+0A|
=14
|18+2A|
=26
|18+3A|
=10
|18+4A|
=0
|18+5A|
=27
|18+8A|
=20
|18+9A|
=9
|18+12A|
=12
|18+19A|
=12
|18+22A|
=9
|18+23A|
=20
|18+26A|
=27
|18+27A|
=0
|18+28A|
=10
|18+29A|
=26
|17+0A|
=10
|17+1A|
=13
|17+3A|
=6
|17+5A|
=23
|17+7A|
=2
|17+8A|
=16
|17+10A|
=0
|17+11A|
=1
|17+20A|
=1
|17+21A|
=0
|17+23A|
=16
|17+24A|
=2
|17+26A|
=23
|17+28A|
=6
|17+30A|
=13
|16+0A|
=8
|16+1A|
=11
|16+7A|
=0
|16+8A|
=14
|16+10A|
=29
|16+12A|
=6
|16+13A|
=19
|16+14A|
=7
|16+17A|
=7
|16+18A|
=19
|16+19A|
=6
|16+21A|
=29
|16+23A|
=14
|16+24A|
=0
|16+30A|
=11
|15+0A|
=8
|15+1A|
=11
|15+7A|
=0
|15+8A|
=14
|15+10A|
=29
|15+12A|
=6
|15+13A|
=19
|15+14A|
=7
|15+17A|
=7
|15+18A|
=19
|15+19A|
=6
|15+21A|
=29
|15+23A|
=14
|15+24A|
=0
|15+30A|
=11
|14+0A|
=10
|14+1A|
=13
|14+3A|
=6
|14+5A|
=23
|14+7A|
=2
|14+8A|
=16
|14+10A|
=0
|14+11A|
=1
|14+20A|
=1
|14+21A|
=0
|14+23A|
=16
|14+24A|
=2
|14+26A|
=23
|14+28A|
=6
|14+30A|
=13
|13+0A|
=14
|13+2A|
=26
|13+3A|
=10
|13+4A|
=0
|13+5A|
=27
|13+8A|
=20
|13+9A|
=9
|13+12A|
=12
|13+19A|
=12
|13+22A|
=9
|13+23A|
=20
|13+26A|
=27
|13+27A|
=0
|13+28A|
=10
|13+29A|
=26
|12+0A|
=20
|12+2A|
=1
|12+5A|
=2
|12+6A|
=4
|12+7A|
=12
|12+8A|
=26
|12+9A|
=15
|12+13A|
=0
|12+18A|
=0
|12+22A|
=15
|12+23A|
=26
|12+24A|
=12
|12+25A|
=4
|12+26A|
=2
|12+29A|
=1
|11+0A|
=28
|11+1A|
=0
|11+2A|
=9
|11+3A|
=24
|11+7A|
=20
|11+9A|
=23
|11+10A|
=18
|11+15A|
=21
|11+16A|
=21
|11+21A|
=18
|11+22A|
=23
|11+24A|
=20
|11+28A|
=24
|11+29A|
=9
|11+30A|
=0
|10+0A|
=7
|10+1A|
=10
|10+5A|
=20
|10+8A|
=13
|10+11A|
=29
|10+12A|
=5
|10+14A|
=6
|10+15A|
=0
|10+16A|
=0
|10+17A|
=6
|10+19A|
=5
|10+20A|
=29
|10+23A|
=13
|10+26A|
=20
|10+30A|
=10
|9+0A|
=19
|9+1A|
=22
|9+2A|
=0
|9+4A|
=5
|9+6A|
=3
|9+11A|
=10
|9+13A|
=30
|9+14A|
=18
|9+17A|
=18
|9+18A|
=30
|9+20A|
=10
|9+25A|
=3
|9+27A|
=5
|9+29A|
=0
|9+30A|
=22
|8+0A|
=2
|8+4A|
=19
|8+5A|
=15
|8+6A|
=17
|8+7A|
=25
|8+9A|
=28
|8+12A|
=0
|8+15A|
=26
|8+16A|
=26
|8+19A|
=0
|8+22A|
=28
|8+24A|
=25
|8+25A|
=17
|8+26A|
=15
|8+27A|
=19
|7+0A|
=18
|7+4A|
=4
|7+5A|
=0
|7+10A|
=8
|7+12A|
=16
|7+13A|
=29
|7+14A|
=17
|7+15A|
=11
|7+16A|
=11
|7+17A|
=17
|7+18A|
=29
|7+19A|
=16
|7+21A|
=8
|7+26A|
=0
|7+27A|
=4
|6+0A|
=5
|6+1A|
=8
|6+3A|
=1
|6+4A|
=22
|6+9A|
=0
|6+11A|
=27
|6+12A|
=3
|6+13A|
=16
|6+18A|
=16
|6+19A|
=3
|6+20A|
=27
|6+22A|
=0
|6+27A|
=22
|6+28A|
=1
|6+30A|
=8
|5+0A|
=25
|5+4A|
=11
|5+6A|
=9
|5+7A|
=17
|5+8A|
=0
|5+10A|
=15
|5+13A|
=5
|5+15A|
=18
|5+16A|
=18
|5+18A|
=5
|5+21A|
=15
|5+23A|
=0
|5+24A|
=17
|5+25A|
=9
|5+27A|
=11
|4+0A|
=16
|4+2A|
=28
|4+3A|
=12
|4+6A|
=0
|4+8A|
=22
|4+11A|
=7
|4+12A|
=14
|4+13A|
=27
|4+18A|
=27
|4+19A|
=14
|4+20A|
=7
|4+23A|
=22
|4+25A|
=0
|4+28A|
=12
|4+29A|
=28
|3+0A|
=9
|3+2A|
=21
|3+6A|
=24
|3+9A|
=4
|3+10A|
=30
|3+11A|
=0
|3+14A|
=8
|3+15A|
=2
|3+16A|
=2
|3+17A|
=8
|3+20A|
=0
|3+21A|
=30
|3+22A|
=4
|3+25A|
=24
|3+29A|
=21
|2+0A|
=4
|2+1A|
=7
|2+3A|
=0
|2+4A|
=21
|2+6A|
=19
|2+9A|
=30
|2+10A|
=25
|2+14A|
=3
|2+17A|
=3
|2+21A|
=25
|2+22A|
=30
|2+25A|
=19
|2+27A|
=21
|2+28A|
=0
|2+30A|
=7
|1+0A|
=1
|1+2A|
=13
|1+3A|
=28
|1+5A|
=14
|1+7A|
=24
|1+11A|
=23
|1+14A|
=0
|1+15A|
=25
|1+16A|
=25
|1+17A|
=0
|1+20A|
=23
|1+24A|
=24
|1+26A|
=14
|1+28A|
=28
|1+29A|
=13
|0+0A|
=0
|0+1A|
=3
|0+2A|
=12
|0+3A|
=27
|0+4A|
=17
|0+5A|
=13
|0+6A|
=15
|0+7A|
=23
|0+8A|
=6
|0+9A|
=26
|0+10A|
=21
|0+11A|
=22
|0+12A|
=29
|0+13A|
=11
|0+14A|
=30
|0+15A|
=24
|0+16A|
=24
|0+17A|
=30
|0+18A|
=11
|0+19A|
=29
|0+20A|
=22
|0+21A|
=21
|0+22A|
=26
|0+23A|
=6
|0+24A|
=23
|0+25A|
=15
|0+26A|
=13
|0+27A|
=17
|0+28A|
=27
|0+29A|
=12
|0+30A|
=3