# Probability of two integers' square sum divisible by $10$

Given two random integers $a$, $b$ calculate probability of $a^2$ + $b^2$ is divisible by $10$.

I've tried to simulate this process and got a result about $0.18$ (maybe incorrect), but have no idea why.

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Whatever your notion of "random integer" may be ... – Hagen von Eitzen Jan 6 '13 at 10:58