Problem #WSP-000527

Problems Algebra

Problem

Let \(n\) be a natural number and \(x=2n^2+n\). Prove that the sum of the square of the \(n+1\) consecutive integers starting at \(x\) is the sum of the square of the \(n\) consecutive integers starting at \(x+n+1\).

For example, when \(n=2\), we have \(10^2+11^2+12^2=13^2+14^2\)!