Square Roots and Su mof Two Squares (involves modulos)

Hello all,

I have a few questions about how squares affect mods. Here they are:

1. Assume p to be an odd prime and a is any integer not congruent to 0 modulo p. It can be proven that the congruence (x^2) __=__ ((-a)^2)(mod p) has solutions IFF p __=__ 1 (mod 4).

How is that proven?

2. Assume there are two numbers c and d where GCD[c,d]=1. If p is any prime number and p|((c^2)+(d^2)), then p __=__ 1 (mod 4),

How is this also proven ?

Any help is greatly appreciated!