olymmath

CMO 1991 Problem 5

  • Day 2

Find all natural numbers nn , such that min⁡k∈N(k2+[n/k2])=1991\min_{k\in \mathbb{N}}(k^2+[n/k^2])=1991 . ( [n/k2][n/k^2] denotes the integer part of n/k2n/k^2 .)

Dataset text AI-MO AoPS. Quoted with source.

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