Hello all, I've been reading up on numbers that are equal to the sum of two squares. As an example, 5 = 4 + 1 = 2^2 + 1^2, and 100 = 64 + 36 = 8^2 + 6^2. There are a few numbers in my book that say they may or may not be perfect squares. They are listed below

A. 7

B. 19

C. 1295

I believe that none of them are sums of squares because I've found no combinations to indicate so. However, I could be wrong.

Here's the catch: The book says that IF the numbers are NOT sums of squares, it can be proven that they aren't by utilizing the number 4. Can anybody help prove this for me for A,B,C (if indeed they are not sums of squares) ?

All help is very much appreciated!