olymmath

ISL 2012 N3

    Determine all integers m≥2m \geq 2 such that every nn with m3≤n≤m2\frac{m}{3} \leq n \leq \frac{m}{2} divides the binomial coefficient (nm−2n)\left(\begin{array}{c}n \\ m-2 n\end{array}\right).

    Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

    Official text: IMO 2012 Shortlist booklet, page 7.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

    Locator isl/2012/n3 · Tag CJKR28FKZV · Edit this page on GitHub · Keys: j next, k previous