The condition requiring that "N" be a multiple of 2"k"+1 is not strictly necessary: there are some further cases for which a solution exists. However, it guarantees a stronger property: if the condition is satisfied, then the set of "k"th powers of any set of "N" numbers in arithmetic progression can be partitioned into two sets with equal sums. This follows directly from the expansion given by the binomial theorem applied to the binomial representing the "n"th element of an arithmetic progression.