MathDB

4

Part of 2024 Regional Olympiad of Mexico Southeast

Problems(1)

Sum of integer sequence and powers of 2

Source: Problem 4 from Regional Olympiad of Mexico Southeast 2024

9/29/2024
Let nn be a non-negative integer and define an=2n−na_n = 2^n - n. Determine all non-negative integers mm such that sm=a0+a1+⋯+ams_m = a_0 + a_1 + \dots + a_m is a power of 2.
Sequencepower of 2number theoryMexicointeger sums