Compositio Mathematica

Research Article

The least common multiple of a quadratic sequence

Javier Cillerueloa1

a1 Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) and Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain (email: franciscojavier.cilleruelo@uam.es)

Abstract

For any irreducible quadratic polynomial f(x) in xs2124[x], we obtain the estimate log l.c.m.(f(1),…,f(n))=nlog n+Bn+o(n), where B is a constant depending on f.

(Received April 29 2010)

(Accepted August 31 2010)

(Online publication December 13 2010)

2000 Mathematics Subject Classification

  • 11N37 (primary)

Keywords

  • least common multiple;
  • quadratic sequences;
  • equidistribution of roots of quadratic congruences

Footnotes

This work was supported by Grant MTM 2008-03880 of MICINN (Spain).