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s_m = x_0 + x_1 + x_2 + ... + x_m is power of 2 , x_n = 2^n-n

Source: 2011 Saudi Arabia Pre-TST February 2.2

January 1, 2022
power of 2Sumnumber theory

Problem Statement

Consider the sequence xn=2n−nx_n = 2^n-n, n=0,1,2,...n = 0,1 ,2 ,.... Find all integers m≥0m \ge 0 such that sm=x0+x1+x2+...+xms_m = x_0 + x_1 + x_2 + ... + x_m is a power of 22.
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