Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T16:15:11.411Z Has data issue: false hasContentIssue false
  • English
  • Français

ON A PROBLEM OF BROCARD

Published online by Cambridge University Press:  02 August 2005

ALEXANDRU GICA  and
LAURENŢIU PANAITOPOL
ALEXANDRU GICA
Affiliation:
University of Bucharest, 14 Academiei St., RO-010014 Bucharest, Romaniaalex@al.math.unibuc.ro, pan@al.math.unibuc.ro
LAURENŢIU PANAITOPOL
Affiliation:
University of Bucharest, 14 Academiei St., RO-010014 Bucharest, Romaniaalex@al.math.unibuc.ro, pan@al.math.unibuc.ro
Get access

Abstract

It is proved that, if $P$ is a polynomial with integer coefficients, having degree 2, and $1>\varepsilon>0$, then $n(n-1)\cdots(n-k+1)=P(m)$ has only finitely many natural solutions $(m,n,k)$, $n\ge k>n\varepsilon$, provided that the $abc$ conjecture is assumed to hold under Szpiro's formulation.

Keywords

11D7511J2511N13
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 4 , August 2005 , pp. 502 - 506
Copyright
© The London Mathematical Society 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)