Descent and the divisibility of elliptic divisibility sequences

The theory of elliptic curves brings about a fascinating overlap between the classical areas of Geometry and Arithmetic. In this proposal, we study the typical factorization of terms of an integer sequence that are generated by simple geometric operations from a starting point on a simple plane curve, called an elliptic curve. The methods build upon techniques developed over many years in the arithmetic of elliptic curves. We expect our results will be applicable in the area of overlap between Number Theory and Logic, specifically the solvability of Diophantine Equations.