The importance of recurrence sequences hardly needs to be explained. Their study is
plainly of intrinsic interest and has been a central part of number theory for many years …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

This volume presents an exhaustive treatment of computation and algorithms for finite fields.
Topics covered include polynomial factorization, finding irreducible and primitive …

Morgan Ward pursued the study of elliptic divisibility sequences, originally initiated by
Lucas, and Chudnovsky and Chudnovsky subsequently suggested looking at elliptic …

Let {F (n)} n∈ N,{G (n)} n∈ N, be linear recurrent sequences. In this paper we are
concerned with the well-known diophantine problem of the finiteness of the set? of natural …

An elliptic divisibility sequence (EDS) is a sequence of integers W_0, W_1, W_2,...
generated by the nonlinear recursion satisfied by the division polyomials of an elliptic curve …

The balancing numbers originally introduced by Behera and Panda [2] as solutions of a
Diophantine equation on triangular numbers possess many interesting properties. Many of …

We classify all linear division sequences in the integers, a problem going back to at least the
1930s. As a corollary we also classify those linear recurrence sequences in the integers for …

We study factorisation in the ring of exponential polynomials and provide a proof of Ritt's
factorisation theorem in modern notation and so generalised as to deal with polynomial …

Let E/k (T) be an elliptic curve defined over a rational function field of characteristic zero. Fix
a Weierstrass equation for E. For points R∈ E (k (T)), write x R= AR/DR 2 with relatively …