2016 APMO Problems/Problem 2
Problem
A positive integer is called fancy if it can be expressed in the form![\[2^{a_1}+2^{a_2}+ \cdots+ 2^{a_{100}},\]](http://latex.artofproblemsolving.com/f/7/0/f70585cad288d934b373c2615570f356c3ca8852.png)
where 
are non-negative integers that are not necessarily distinct. Find the smallest positive integer 
such that no multiple of is a fancy number.
