congruence in integer #2

**Deepu** · February 1st 2010, 08:44 PM

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

**tonio** · February 2nd 2010, 03:24 AM

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

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