# 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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