# Math Help - congruence in integer #2

1. ## congruence in integer #2

Prove or disprove: if a^2=b^2=mod(n) and n is prime then a=b(mod n) or a=-b(mod n).

2. Originally Posted by Deepu
Prove or disprove: if a^2=b^2=mod(n) and n is prime then a=b(mod n) or a=-b(mod n).

True: $a^2=b^2\!\!\!\pmod n \Longleftrightarrow (a-b)(a+b)=0\!\!\!\pmod n$ $\Longleftrightarrow a-b=0\!\!\!\pmod n\,\,\,or\,\,\,a+b=0\!\!\!\pmod n$ , since n is prime.

Tonio