suppose p is an odd prime and $a$ and $b$ are positive integers such that $ p^5 \mid a^2 + b^2 $ and $ p^5 \mid a(a + b)^2$. Show that not necessarily $p^5 \mid a(a + b) $. I'm not getting anything productive
2026-04-02 12:23:48.1775132628
Show that not necessarily $p^5 \mid a(a + b) $.
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You just need to find some values. For example p = 5, a = 25, b = 50