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math.NT2009
The divisibility of a^n-b^n by powers of n
Chris Smyth
For given integers a,b, and j at least 1 we determine the set of integers n for which a^n-b^n is divisible by n^j. For j=1,2, this set is usually infinite; we find explicitly the e…
math.NT2009★ 4 cited
Integer symmetric matrices of small spectral radius and small Mahler measure
James McKee, Chris Smyth
In a previous paper we completely described cyclotomic matrices--integer symmetric matrices of spectral radius at most 2. In this paper we find all minimal noncyclotomic matrices.…
math.AG2009
Euclid meets Bezout: Intersecting algebraic plane curves with the Euclidean algorithm
Jan Hilmar, Chris Smyth
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.