Andrew Granville's Home Page

1985 Publications

Refining the conditions on the Fermat quotient
Mathematical Proceedings of the Cambridge Philosophical Society, 98 (1985), 5-8

We showed that if \( q^{p-1}\equiv 1 \pmod {p^2}\) for all sufficiently large primes \( p\), then \( q^{p-1}\equiv 1 \pmod {p^3}\) for infinitely many primes \( p\).


The set of exponents, for which Fermat's Last Theorem is true, has density one
Comptes Rendus de l'Académie des Sciences du Canada, 7 (1985), 55-60

We proved the result in the title as a consequence of Faltings' Theorem. This was proved, more-or-less simultaneously, by Heath-Brown