# True?: Let $(n, m)$ be an arbitrary Amicable Pair. Then $n$ is odd iff its last digit is $5$

I believe I've found all Amicable Pairs $(n, m)$ such that n is in the closed interval $[1, 34000000]$. Here's my list.

By inspection I believe that for all $n$ in the list, $n$ is odd iff its last digit is $5$. Can it be proved that this is true for all Amicable Pairs?

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I think the first counterexample $(n,m)$ with $n < m$ where $n$ is odd and not congruent to $5$ mod $10$ is $(34765731, 36939357)$, which by misfortune is just outside your search region.