V.I.Arnold.
Several talks at the seminar in Moscow. Autumn 2002.

Let n be an odd integer.
We say that n belongs to the class (N+) if
2^{\phi(n)/N}=1 (mod n), where phi(n) is Euler's function
(number of residues modulo n mutually prime with n).
We say that n belongs to the class (M-) if
2^{\phi(n)/M}=-1 (mod n).
The talks are about several hundred theorems describing the 
properties of the sets of integers (N+) and (M-) for various
values of N and M.