Andrew Granville's Home Page

1987 Publications

Sophie Germain's Theorem for prime pairs \( p, 6p+1\)
Journal of Number Theory, 27 (1987), 63-72

We develop the first case of Fermat's Last Theorem for exponent \( p\) in the case where \( p\) and \( 6p+1\) are prime (so that Sophie Germain's proof does not directly apply).


Matrices as the sum of four squares
Linear and Multilinear Algebra, 20 (1987), 247-251

We show that every integral \( n\)-by-\( n\) matrix is the sum of four squares, for each \( n\geq 2\).


On Hajos' Conjecture, (with Alexandros Moisiadis)
Congressus Numerantium, 56 (1987), 183-187

For any simple Eulerian graph of order \( n\) and maximum degree \( \leq 4\) we show that one needs \( \leq (n-1)/2\) edge disjoint cycles to partition the edges of the graph.