## Unique Square Sum

#### Problem

You are given that ALL primes that are one more than a multiple of 4 can be written as the sum of two squares. For example, 13 = 2^{2}+3^{2}.

Assuming that a prime is expressible as the sum of two squares, prove that it can be done in only one way.

Problem ID: 176 (May 2004) Difficulty: 4 Star