> # ICTMT5talk.mws

Fermat's little theorem, ICTMT5, Klagenfurt University, Austria. August 2001.

Section 1. The use of ' little ', the theorem itself, and how it originated.

Section 2. Decimal (and other) expansions of rational numbers.

Section 3. Quadratic and other congruences. Mersenne and Fermat numbers.

Section 4. Primality testing.

Section 5. RSA public-key cryptography.

Section 6. Factoring. The Pollard ( ) factoring method.

Section 7. Open problems: Artin's conjecture, Giuga's conjecture.

Artin's conjecture (primitive roots).

Giuga's conjecture (a type of converse) .

Section 8. Proofs of some important consequences of Fermat's 'little' theorem.

Section 9. Bibliography and web references.