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(2^m -1)^2 | 2^n-1 iff m(2^m-1) |n - All-Russian MO 1997 Regional (R4) 10.3

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September 24, 2024
number theorydivisibledivides

Problem Statement

Natural numbers mm and nn are given. Prove that the number 2n−12^n-1 is divisible by the number (2m−1)2(2^m -1)^2 if and only if the number nn is divisible by the number m(2m−1)m(2^m-1).
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