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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
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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

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