1987 OIM Problems/Problem 3

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Problem

Prove that if $m$, $n$, and $r$ are non-zero positive integers, and \[1+m+n\sqrt{3}=[2+\sqrt{3}]^{2r-1}\] then $m$ is a perfect square.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe2.htm