700 Followers prob!

Let f(x)=12+22+32++(x1)2+x2f(x) = \sqrt{1^{2} + 2^{2} + 3^{2} + \cdots + (x-1)^{2} + x^{2}} .

Find the minimum value of n2n \geq2 such that f(n)f(n) is a positive integer.

nn is a positive integer.

Clarification: f(x)f(x) denote the square root of the sum of the squares of first xx positive integers.

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