# Fraction of a fraction

Number Theory Level 4

$\large 1+\frac { x-1 }{ 2+\frac { x-1 }{ 2+\frac { x-1 }{ 2+\ddots } } }$

For integer $$1\le x\le 2015$$, find the number of $$x$$ such that the infinitely nested fraction above is an integer.

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