# USAMO Problem 2

What is the smallest integer $$n$$, greater than one, for which the root-mean-square of the first $$n$$ positive integers is an integer?

$$\mathbf{Note.}$$ The root-mean-square of $$n$$ numbers $$a_1, a_2, \cdots, a_n$$ is defined to be $\left[\frac{a_1^2 + a_2^2 + \cdots + a_n^2}n\right]^{1/2}$

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