Let $S$ be the set of the integers that can be represented as the sum of two squares. $S={0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, ...}$. I have made this hypothesis: If an integer is in set $S$ but it can be represented as a sum of squares with two different ways, then this number is not prime. I have found Fermat's theorem on sums of two squares but I have not a proper proof on that. Any help would be appreciated.
2026-03-30 07:55:53.1774857353
Sum of squares and primes
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