Integers representable as differences of linear recurrence sequences

Robert Tichy, Ingrid Vukusic, Daodao Yang, Volker Ziegler*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let {Un}n≥0 and {Vm}m≥0 be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [- x, x] which can be represented as differences U n- V m. In particular, the density of such integers is 0.

Original languageEnglish
Article number24
JournalResearch in Number Theory
Issue number2
Early online date18 Mar 2021
Publication statusPublished - Jun 2021


  • math.NT
  • Pillai’s problem
  • Diophantine equations
  • Recurrence sequence

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this