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A positive integer is called fancy if it can be expressed in the form

2^{a_1}+2^{a_2}+ \cdots+ 2^{a_{100}},

where

a_1,a_2, \cdots, a_{100}

are non-negative integers that are not necessarily distinct. Find the smallest positive integer

n

such that no multiple of

n

is a fancy number.
Senior Problems Committee of the Australian Mathematical Olympiad Committee

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