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Prove that $n$ is a sum of two squares?

I was reading this and began wondering if there is a general theorem that a number of a given form is the sum of two squares. I know about Fermat's Theorem, but I am thinking about the general case. The question is

For which positive integer $n$ we can find positive integers $a,b$ with $n=a^2+b^2$?

I found a related question: Prove that $n$ is a sum of two squares?

If this is a duplicate, I am sorry. I have searched the site and didn't find this question posted. Any reference would be useful.

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    See [Fermat's theorem on sums of two squares](http://en.wikipedia.org/wiki/Fermat's_theorem_on_sums_of_two_squares). It has been said that is the result Fermat was most proud of.2011-06-13

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The answer is on the page you linked to: $n$ is a sum of two squares if and only if $n$ is a square times a product of different primes which are either 1 modulo 4 or 2.

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    Perhaps part of the confusion comes from not realizing that **every** positive integer has a **unique** decomposition as a square times a product of different primes (product over a possibly empty set of primes).2011-06-13