Fun Little Problem

[rabbit]

Suppose that m is either a power p^a of a prime p > 2 or else twice an odd prime power.  Prove that if x² congruent 1 mod m, then either
x congruent 1 mod m
or
x congruent -1 mod m





Have fun

[Ender]

I need clarification on the givens

Suppose that m is either a power p^a of a prime p > 2

So m = p^a

or else twice an odd prime power.

Twice an odd prime power? Do you mean m = 2x^y where x is prime? Or do you mean m = 2a, referring to the first given, where m = p^a

[rabbit]

1. Yes.

2. There is no prime which has an integer as a square root   I mean 2a.