SIMON-MARAIS 2022 B1

Paper B

Let $A > 1$ be a real number. Determine all pairs $(m, n)$ of positive integers for which there exists a positive real number $x$ such that $(1 + x)^m = (1 + Ax)^n$ .

Official text Simon Marais Mathematics Competition 2022 official paper, page 2. Quoted with source.

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