We derive sharp upper bounds for the size of the intersection of certain linear recurrence sequences. As a consequence of these, we partially resolve a conjecture of Yuan on simultaneous Pellian equations, under the condition that one of the parameters involved is suitably large.

Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9 or less, Positivity is decidable, with complexity in the Counting Hierarchy.

The number of ramified coverings of the sphere by the double torus, and a general form for higher genera * Abstract An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ramification type over infinity. Thus we are able to determine various linear recurrence equations for ...

We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical points of sampled actions. Then we characterize the discretization operators such that, for all quadratic lagrangian, the discrete Euler-Lagrange equations co...

Richard Stanley St96] has recently narrated the fascinating story of how the classical Schrr oder Sch1870] numbers s(n) are even more classical than has been believed before. They (at least s(10) = 103049) have been known to Hipparchus (190-127 B.C.). Stanley recalled the three-term linear recurrence ((Co64]; Co74], p. 57) (1) 3(2n ? 1)s(n) = (n + 1)s(n + 1) + (n ? 2)s(n ? 1) (n 2); s(1) = s(2)...

We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomi...

We study discrete almost automorphic functions sequences defined on the set of integers with values in a Banach space X. Given a bounded linear operator T defined on X and a discrete almost automorphic function f n , we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation Δu n Tu n f n . We also prove the existence of a discrete almost autom...

Abstract. Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equations. Finite difference schemes for the ap...

The question of which terms of a recurrence sequence fail to have primitive prime divisors has been significantly studied for several classes of linear recurrence sequences and for elliptic divisibility sequences. In this paper, we consider the question for sequences generated by the iteration of a polynomial. For two classes of polynomials f(x) ∈ Z[x] and initial values a1 ∈ Z, we show that th...

Global attractivity in a quadratic-linear rational difference equation with delay C.M. Kent & H. Sedaghat To cite this article: C.M. Kent & H. Sedaghat (2009) Global attractivity in a quadratic-linear rational difference equation with delay, Journal of Difference Equations and Applications, 15:10, 913-925, DOI: 10.1080/10236190802040992 To link to this article: http://dx.doi.org/10.1080/1023619...