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Cyclic permutation of binary numbers

Source: Romania 2018 TST Problem 3 Day 3

May 25, 2020
Binarycombinatoricspermutation

Problem Statement

For every integer n≥2n \ge 2 let BnB_n denote the set of all binary nn-nuples of zeroes and ones, and split BnB_n into equivalence classes by letting two nn-nuples be equivalent if one is obtained from the another by a cyclic permutation.(for example 110, 011 and 101 are equivalent). Determine the integers n≥2n \ge 2 for which BnB_n splits into an odd number of equivalence classes.
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