### 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).

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#### 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 $$n\geq 2$$.

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#### 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.

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