olymmath

RU-ALLRUSSIAN 1982 Problem 3

    N is a sum of n powers of 2. If N is divisible by 2m−12^{\mathrm{m}} - 1 , prove that n≥m\mathrm{n} \geq \mathrm{m} . Does there exist a number divisible by 11...1 (m 1s) which has the sum of its digits less than m?

    Dataset text NuminaMath olympiads. Quoted with source.

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