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\sqrt{(1^2+2^2+...+n^2)/n}$ is an integer.

Source: Singapore Open Math Olympiad 2017 2nd Round p3 SMO

March 26, 2020

Integernumber theorySumSum of Squares

Problem Statement

Find the smallest positive integer

n

so that

\sqrt{\frac{1^2+2^2+...+n^2}{n}}

is an integer.