If $p$ is a prime number expressible as $x^2$ + $1$, is it possible to rewrite $p$ as $p$=$a^2$ + $b^2$ where $a,b >1$? If so can you give me an example?
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Can you show some investigation attempts on this problem. For example, have you checked to see if this is possible for some non-prime numbers? – barak manos Oct 12 '15 at 09:31
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No, you don't understand the question. – unknownMe Oct 12 '15 at 09:36
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@Shailesh jevie wants a new representation not the excisting one – Konstantinos Gaitanas Oct 12 '15 at 10:00
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This question has an answer here where it is shown that if $n$ can be expressed as a sum of two squares in two ways then $n$ must be composite.
I think it was Mersenne who was first to prove this but I am not sure.
(So, the answer to your question is NO)
Konstantinos Gaitanas
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