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(2^m-1)^2|2n-1 iff m(2^m-1)|n

Source: S&M 2002 2nd Grade P3

May 14, 2021
number theoryDivisibility

Problem Statement

Let mm and nn be positive integers. Prove that the number 2n−12n-1 is divisible by (2m−1)2(2^m-1)^2 if and only if nn is divisible by m(2m−1)m(2^m-1).
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