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IMO Shortlist 2012, Number Theory 3

Source: IMO Shortlist 2012, Number Theory 3

July 26, 2013
number theoryprime numbersbinomial coefficientsIMO Shortlist

Problem Statement

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)\binom{n}{m-2n}.
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