let-give-a-prime-number-p-gt-2-and-a-D-a-p-1-and-suppose-that-the-equation-x-2-a-p-have-a-solution1-1-prove-that-a-p-1-2-1-p-2-prove-that-x-2-1-p-p-1-4-

Question Number 29035 by abdo imad last updated on 03/Feb/18

l e t g i v e a p r i m e n u m b e r p > 2 a n d a / D (a, p) = 1 a n d

s u p p o s e t h a t t h e e q u a t i o n x^{2} \equiv a [p] h a v e a s o l u t i o n 1)

1) p r o v e t h a t a^{\frac{p - 1}{2}} \equiv 1 [p]

2) p r o v e t h a t x^{2} \equiv - 1 [p] \Leftrightarrow p \equiv 1 [4]