Freeflows

Triangular Number Puzzle

For a positive integer $ n $, the $ n^{th} $ 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 $.

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$\frac{a}{b}$
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0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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