There is a theorem that if a natural number n is a sum of two squares of rational numbers, then n is also a sum of two squares of integers. A proof could involve Fermat's theorem on sums of two squares, but the proof of that theorem in itself is quite lengthy, so that the whole proof will be quite lengthy if you don't just take Fermat's theorem for granted.
Does anyone know if a short(er) proof exists that if n is the sum of two rational squares, it's also the sum of two integral squares? Thanks.
There is a theorem that if a natural number n is a sum of two squares of rational numbers, then n is also a sum of two squares of integers. A proof could involve Fermat's theorem on sums of two squares, but the proof of that theorem in itself is quite lengthy, so that the whole proof will be quite lengthy if you don't just take Fermat's theorem for granted.
Does anyone know if a short(er) proof exists that if n is the sum of two rational squares, it's also the sum of two integral squares? Thanks.