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Sum os several powers of two

Source: Romania TST 2023 Day 1 P1

April 7, 2024
number theorysum of digits

Problem Statement

Let mm and nn be positive integers, where m<2n.m < 2^n. Determine the smallest possible number of not necessarily pairwise distinct powers of two that add up to m⋅(2n−1).m\cdot(2^n- 1).
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