Question 17

Number Theory Level pending

For a positive integer \(n,\) the \(n^{th}\) triangular number is \(T(n)=\frac{n(n+1)}{2}.\) For example, \(T(3)=\frac{3\times4}{2}=6,\) so the third triangular number is \(6.\)

Find the smallest integer \(b>2011\) such that \(T(b+1)-T(b)=T(x)\) for some positive integer \(x.\)

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