International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 521-528
doi:10.1155/S0161171297000719
Multiplicative polynomials and Fermat's little theorem for non-primes
Paul Milnes1
and C. Stanley-Albarda2
1Department of Mathematics, University of Western Ontario, Ontario, London N6A 5B7, Canada
2Department of Mathematics, University of Toronto, Ontario, Toronto M5S 1A1, Canada
Abstract
Fermat's Little Theorem states that xp=x(modp) for x∈N and prime p, and so identifies an integer-valued polynomial (IVP) gp(x)=(xp−x)/p. Presented here are IVP's gn for non-prime n that complete the sequence {gn|n∈N} in a natural way. Also presented are characterizations of the gn's and an indication of the ideas from topological dynamics and algebra that brought these matters to our attention.