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min pos. integer n = sum of diff. perfect squares, with sum =2014

Source: Finland 2014, Problem 5

September 1, 2019
minimumPerfect SquaresSumnumber theorycombinatorics

Problem Statement

Determine the smallest number n∈Z+n \in Z_+, which can be written as n=Σa∈Aa2n = \Sigma_{a\in A}a^2, where AA is a finite set of positive integers and Σa∈Aa=2014\Sigma_{a\in A}a= 2014. In other words: what is the smallest positive number which can be written as a sum of squares of different positive integers summing to 20142014?
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