Triangular Number

For a positive integer n , the nth  triangular number is \(T(n)=\dfrac{n(n+1)}{2}.\)

For example, \(T(3) = \frac{3(3+1)}{2}= \frac{3(4)}{2}=6\) , so the third triangular number is 6.

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