OIM 1987 Problem 3

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

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.