chapter 9

10 Pages

## Mersenne and Fermat

We have seen that if n is a composite, then M (n) is also composite. For if n = rs, then

2n — 1 = (2ry - 1 = (2r - l ) (2 r(s-1) + 2r(s-2) + • • • + T + 1). Hence M (r) is a factor of M (n) — M {rs) . Of course, M {s) is also a factor of M(n) .