# Development ofAlgorithmic Constructions

 12:27:09 19.Sep 2021

29 31 33
√2 √3 √5 √6 √7 √8

 Number p= Adjoined square root=

### Calculation

A=√3
(a+bAI)² = a²-b²A² + 2abAI mod p
|(a+bAI)| = (a+bAI)(a-bAI) = a²+b²A² mod p

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

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

 30 0 30√3
Number of elements = 30

### Number = 31, Adjoined = √3, Exponent = 1, 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

 |30+12AI|=30 |30+19AI|=30 |29+9AI|=30 |29+22AI|=30 |28+10AI|=30 |28+21AI|=30 |24+2AI|=30 |24+29AI|=30 |22+13AI|=30 |22+18AI|=30 |21+7AI|=30 |21+24AI|=30 |16+11AI|=30 |16+20AI|=30 |15+11AI|=30 |15+20AI|=30 |10+7AI|=30 |10+24AI|=30 |9+13AI|=30 |9+18AI|=30 |7+2AI|=30 |7+29AI|=30 |3+10AI|=30 |3+21AI|=30 |2+9AI|=30 |2+22AI|=30 |1+12AI|=30 |1+19AI|=30 |0+14AI|=30 |0+17AI|=30