700 Followers prob!

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.

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