BMO Round 1, 2026

Number theory Difficulty 6.0 National Olympiad Prove it United Kingdom

A ramp is a sequence of three different positive integers $a$ , $b$ , $c$ such that $a$ is a factor of $b$ and $b$ is a factor of $c$ . For every prime number $p$ and every positive integer $n$ , determine with proof whether $p^n$ can be expressed as the sum of a ramp.

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