# 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
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## 1 Answer

Final digit of a and b as follows

(0,0); (1,3)(1,7); (2,4)(2,6); (3,1)(3,9); (4,2)(4,8); (5,5); (6,2)(6,8); (7,1)(7,9); (8,4)(8,6); (9,3)(9,7)

That's 18 possibilities out of 100

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Oh, thanks. It is so clear and I should had figured it out. –  halfelf Jan 6 '13 at 9:20
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