IMO Shortlist 1990 problem 21


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2. travnja 2012.
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Let n be a composite natural number and p a proper divisor of n. Find the binary representation of the smallest natural number N such that

\frac{(1 + 2^p + 2^{n-p})N - 1}{2^n}

is an integer.
Izvor: Međunarodna matematička olimpijada, shortlist 1990