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Number Theory Level 4

Let $f(x) = \sqrt{1^{2} + 2^{2} + 3^{2} + \cdots + (x-1)^{2} + x^{2}}$ .

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

$n$ is a positive integer.

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