Thread: Sum of 3 squares

I apologize for re-posting this question, but someone answered yesterday without reading the entire problem and nobody else seems to be looking at it. Thanks.

Prove that if a prime number is a sum of three squares of different primes, then one of the primes must be equal to 3.

Here's a thought:

Try showing is composite when are prime.

So we have where are all distinct primes.

Assume

This means , which is a contradiction.