Andrew Granville's Home Page

1988 Publications

The First Case of Fermat's Last Theorem is true for all prime exponents up to \( 714,591,416,091,389\) (with Michael B. Monagan)
Transactions of the American Mathematical Society, 306 (1988), 329-359 .

We show that if the first case of Fermat's Last Theorem is false for prime exponent \( p\) then \(p^2\) divides \( q^p-q\) for all primes \( q\leq 89\). The title theorem follows.


On Sophie Germain type criteria for Fermat's Last Theorem (with Barry J. Powell)
Acta Arithmetica, 50 (1988), 265-277.

Variations on Sophie Germain's Theorem


Nested Steiner \( n\)-cycle systems and perpendicular arrays (with Alexandros Moisiadis and Rolf Rees)
Journal of Combinatorial Mathematics and Mathematical Computing , 3 (1988), 163-167.

We prove that for any odd \( n>1\) and sufficiently large \( m\) there exists a nested Steiner \(n\)-cycle system of order \( m\) if and only of \( m\equiv 1 \pmod {2n}\).


Bipartite planes (with Alexandros Moisiadis and Rolf Rees)
Congressus Numerantium, 61 (1988), 241-248.

For which integers \( s,t, n=2st\) does there exist a decomposition of the complete graph on \( n\) vertices into \( n-1\) copies of the complete \( (s,t)\)-bipartite graph?