Use the formula for r2n to prove the given- if n p where p

Question

Use the formula for r₂(n) to prove the following:

(a) If n = p, where p is a prime of the form 4k + 1, then r₂(n) = 8. This implies that n can be written in a unique way as n = n₁² + n₂², except for the signs and reordering of n₁ and n₂.

(b) If n = q^a, where q is prime of the form 4k + 3 and a is a positive integer, then r₂(n) > 0 if and only if a is even.

(c) In general, n can be represented as the sum of two squares if and only if all the primes of the form 4k + 3 that arise in the prime decomposition of n occur with even exponents.