Matrix divisibility sequences

We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated to groups of maps on affine spaces.Comment: 10 page

A Generalization of Siegel's Theorem and Hall's Conjecture

Consider an elliptic curve, defined over the rational numbers, and embedded in projective space. The rational points on the curve are viewed as integer vectors with coprime coordinates. What can be said about a rational point if a bound is placed upon the number of prime factors dividing a fixed coordinate? If the bound is zero, then Siegel's Theorem guarantees that there are only finitely many such points. We consider, theoretically and computationally, two conjectures: one is a generalization of Siegel's Theorem and the other is a refinement which resonates with Hall's conjecture.Comment: 11 pages, 5 table

Obituary: Graham Everest 1957-2010

Obituary of Graham Everest (1957-2010

Prime power terms in elliptic divisibility sequences

We consider a particular case of an analog for elliptic curves to the Mersenne problem : finding explicitely all prime power terms in an elliptic divisibility sequence when descent via isogeny is possible. We explain how this question can be related to classical problems in diophantine geometry and we compute an explicit upper bound on the index of prime power terms in magnified elliptic divisibility sequences.Comment: 30 pages, submitte