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11 6 $begingroup$ Which rational numbers can be written as the sum of two rational squares? That is, for which rational numbers $a$, are there rational numbers $x$ and $y$ such that $a = x^2 + y^2$. It is a famous theorem that if an integer can be written as the sum of two rational squares then it can be written as the sum of two integral squares, and then the solution is the famous one by Fermat, but I didn't find anything about the general case. number-theory share | cite | improve this question edited Sep 21 '15 at 14:00 lhf