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$a|(2b+a)^2$ and $a$ is odd implies $a|b$?

I would say that: $$ a|(2b+a)^2 $$ $$ a|4b^2+4ab+a^2 $$ $$ a|4b^2$$ $$ a|b^2$$ But I don't think that this means that $a|b$, does it? How can I prove that $a|b$, if it's possible? Thanks

5 Answers 5