MathDB

10.3

Part of 1997 All-Russian Olympiad Regional Round

Problems(1)

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

Source:

9/24/2024
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).
number theorydivisibledivides