Fermat's theorem
Since the Diophantus identity implies that the product of two integers each of which can be written as the sum of two squares is itself expressible as the sum of two squares, by applying Fermat's theorem to the prime factorization of any positive integer "n", we see that if all the prime factors of "n" congruent to 3 modulo 4 occur to an even exponent, then "n" is expressible as a sum of two squares. The converse also holds. This generalization of Fermat's theorem is known as the sum of two squares theorem.