Question 66
For every integer $n \ge 2$, let $B_n$ denote the set of all binary $n$-tuples of zeroes and ones, and split $B_n$ into equivalence classes by letting two $n$-tuples be *equivalent* if one is obtained from the other by a cyclic permutation of the entries. Determine the integers $n \ge 2$ for which $B_n$ splits into an odd number of equivalence classes.