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.

Article

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

Article

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 $$m\equiv 1 \pmod {2n}$$.

Article

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?

Article