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China Mathematical Olympiad 1991 problem5

Source: China Mathematical Olympiad 1991 problem5

October 8, 2013
floor functionnumber theory unsolvednumber theory

Problem Statement

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.)
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