olymmath

USAMO 2025 Problem 5

  • Day 2

Determine, with proof, all positive integers kk such that 1n+1∑i=0n(ni)k\frac{1}{n+1} \sum_{i=0}^n \binom{n}{i}^k is an integer for every positive integer n.n.

Dataset text AI-MO AoPS. Quoted with source.

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