MathDB

21

Part of 1990 IMO Shortlist

Problems(1)

[(1 + 2^p + 2^{n-p})N - 1] / 2^n

Source: IMO ShortList 1990, Problem 21 (ROM 1)

8/15/2008
Let n n be a composite natural number and p p a proper divisor of n. n. Find the binary representation of the smallest natural number N N such that \frac{(1 \plus{} 2^p \plus{} 2^{n\minus{}p})N \minus{} 1}{2^n} is an integer.
number theoryDivisibilitybinary representationminimizationIMO Shortlist