Andrew Granville's Home Page

1994 Publications

There are infinitely many Carmichael numbers (with Red Alford and Carl Pomerance)
Annals of Mathematics, 140 (1994), 703-722.

We establish that there are \(\gg x^{2/7}\) Carmichael numbers up to \( x\).


On sparse languages \( L\) such that \( LL=\sum^*\) (with Per Enflo, Jeffrey Shallit and Sheng Yu)
Discrete Mathematics, 52 (1994), 275-285.

We give various examples of sparse languages \( L\) for which \( LL \) yields all possible words made from the given alphabet


On the difficulty of finding reliable witnesses (with Red Alford and Carl Pomerance)
Algorithmic Number Theory, (ANTS-I proceedings, eds L.M. Adleman and M.D. Huang), Lectures Notes in Computer Sci., 877 (1994), 1-16.

We show that for any finite set of primes there are infinitely many Carmichael numbers that are also strong pseudoprimes with respect to the base given by each of the finite set of primes


The Status of Fermat's Last Theorem — mid 1994 (with Michael Monagan )
Maple in Mathematics and Sciences, (1994), 6-9.

A journalistic article on the state of FLT at that time