Formula

pytheagle

Let $p$ be a prime of the form $4k+3$ where $k$ is a nonnegative integer. Then, if $p^{2n+1}|a^2+b^2$ , both $a$ and $b$ must be divisible by $p$ .

My friend told me about this formula (or maybe something similar, I forgot), and I've been trying to prove it with no success. I would appreciate it if someone would post a proof (or the name of the formula, so I can Google the proof).

**Posted:** Fri Nov 06, 2009 4:34 pm

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t0rajir0u

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**Posted:** Fri Nov 06, 2009 5:54 pm

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pytheagle

I'm sorry, but only the first sentence was simple enough for me to understand. Sad

Could you please explain it a bit more simply? (I'm not smart enough to understand you.)

**Posted:** Fri Nov 06, 2009 6:55 pm

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t0rajir0u

Are you familiar with modular arithmetic and quadratic residues?

**Posted:** Sat Nov 07, 2009 1:37 pm

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