If p prime and if $p = 1 \pmod{4}$, then $p = a^2 + b^2$; why must $a$ or $b$ be a square mod $p$?
For $p$ prime, $p = a^2 + b^2$, why must $a$ or $b$ be a square?
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number-theory
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07 is a prime. Yet 7=/=1mod4. – 2011-11-03
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0I was unclear, I meant "if $p$ is a prime and if $p = 1 \pmod{4}$, then...", not "if $p$ is a prime, then $p = 1 \pmod{4}$ and..." . – 2011-11-03
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0I don't even think this is correct. 7=? you can't write 7 in that form yet 7 is a prime. – 2011-11-03
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0$7=3 \pmod{4}$. – 2011-11-03
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0It's easy if I knew that. Take $a^2+b^2$ mod 4 and that work out what the possibilities. – 2011-11-03