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{0,1,...,2k+1}, odd zeroes

Source: Serbia & Montenegro 2001 3,4th Grade P3

June 2, 2021
combinatorics

Problem Statement

Let kk be a positive integer and NkN_k be the number of sequences of length 20012001, all members of which are elements of the set {0,1,2,…,2k+1}\{0,1,2,\ldots,2k+1\}, and the number of zeroes among these is odd. Find the greatest power of 22 which divides NkN_k.
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