# 700 Followers prob!

**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.