Problem

Source: Finland 2014, Problem 5

Tags: minimum, Perfect Squares, Sum, number theory, combinatorics



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