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Omni-MATH / 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 …

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What is the smallest integer nn , greater than one, for which the root-mean-square of the first nn positive integers is an integer? $\mathbf{Note.}$ The root-mean-square of nn numbers a1,a2,,ana_1, a_2, \cdots, a_n is defined to be [a12+a22++an2n]1/2\left[\frac{a_1^2 + a_2^2 + \cdots + a_n^2}n\right]^{1/2}
Plain-text mathematical notation (without MathML)
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 a₁,a₂,⋯,a_(n) is defined to be [(a₁²+a₂²+⋯+a_(n)²)/(n)]^(1/2)
Original LaTeX notation
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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