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Found problems: 1

2023 Euler Olympiad, Round 2, 1
Tags: number theory , algebra , euler , 100 , power of 2 , residue
Consider a sequence of 100 positive integers. Each member of the sequence, starting from the second one, is derived by either multiplying the previous number by 2 or dividing it by 16. Is it possible for the sum of these 100 numbers to be equal to $2^{2023}$? [i]Proposed by Nika Glunchadze, Georgia[/i]