Suppose that m is either a power p[sup]a[/sup] of a prime p > 2 or else twice an odd prime power.  [u]Prove[/u] that if x[sup]2[/sup] congruent 1 mod m, then either
x congruent 1 mod m
or
x congruent -1 mod m





Have fun :)

I need clarification on the givens

[quote author=rabbit link=topic=13196.msg133451#msg133451 date=1131663500]
Suppose that m is either a power p[sup]a[/sup] of a prime p > 2
[/quote]

So m = p[sup]a[/sup]

[quote author=rabbit link=topic=13196.msg133451#msg133451 date=1131663500]
or else twice an odd prime power.
[/quote]

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

1. Yes.

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