Cyclotomic identity

In mathematics, the cyclotomic identity states that

where M is Moreau's necklace-counting function

and μ is the classic Möbius function of number theory. The denominator on the right, 1 − z ^j, is a cyclotomic polynomial -- hence the name.

Reference

Nicholas Metropolis & Gian-Carlo Rota. The Cyclotomic Identity. Reprinted in Gian-Carlo Rota on Combinatorics. Birkhäuser. Boston. 1995.