
Congruence Problem
This is from chapter on linear congruences:
Show that if p is an odd prime and a is a positive integer not divisible by p, then the congruence $\displaystyle x^2 \equiv a \pmod {p}$ has either no solution or exactly two incongruent solutions.
I can see If $\displaystyle p \mid x$, then there are no solutions. I'm really not sure how to approach the rest of this...

Re: Congruence Problem
Solving the 'quadratic congruence equation'...
$\displaystyle x^{2} \equiv a (\text{mod}\ p)$ (1)
... is equivalent to find two integers x < p and y so that is...
$\displaystyle a + p\ y = x^{2}$ (2)
Now if $\displaystyle x_{0}$ satisfies (2) for some y, then $\displaystyle x_{1} = px_{0} \ne x_{0} $ satisfies also (2) for some other y...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$