Igor Shparlinski (Sydney)
We describe recent results improving previous estimates
of H. W. Lenstra and A. Granville on the smallest non-zero
Fermat quotient. This question is motivated by applications
to square-free testing (H. W. Lenstra, 1979), Fermat Last
Theorem (A. Granville, 1991) and algebraic number theory
and coding theory (Y. Ihara, 2006).
This is joint work with Jean Bourgain, Kevin Ford, and Sergei Konyagin.