Intersections of recurrence sequences

Intersections of Recurrence Sequences

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.

Recurrence Sequences

Introduction 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. Moreover, these sequences appear almost everywhere in mathematics and computer science. For example, the theory of power series representing rational functions [55], pseudo-random number generators ([48], [49]...

Intersections of Second - Order Linear Recursive Sequences

Primes in Intersections of Beatty Sequences

In this note we consider the question of whether there are infinitely many primes in the intersection of two or more Beatty sequences ⌊ξjn+ ηj⌋, n ∈ N, j = 1, . . . , k. We begin with a straightforward sufficient condition for a set of Beatty sequences to contain infinitely many primes in their intersection. We then consider two sequences when one ξj is rational. However, the main result we est...

Zeros of linear recurrence sequences

Let f (x) = P0(x)α 0 + · · · + Pk(x)α k be an exponential polynomial over a field of zero characteristic. Assume that for each pair i, j with i 6= j , αi/αj is not a root of unity. Define 1 = ∑kj=0(deg Pj +1). We introduce a partition of {α0, . . . , αk} into subsets { αi0, . . . , αiki } (1 ≤ i ≤ m), which induces a decomposition of f into f = f1 +· · ·+fm, so that, for 1 ≤ i ≤ m, (αi0 : · · ·...