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Part of 1990 IMO Longlists

Problems(1)

There exist infinitely many positive integers - ILL1990 ICE1

Source:

Prove that there exist infinitely many positive integers

1

such that the number

\frac{1^2+2^2+\cdots+n^2}{n}

is a perfect square. Obviously,

1

is the least integer having this property. Find the next two least integers having this property.

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