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    Helou, C. and Haddad, L. 2008. A note on a problem of Brocard-Ramanujan. The Ramanujan Journal, Vol. 17, Issue. 2, p. 155.


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  • Bulletin of the London Mathematical Society, Volume 37, Issue 4
  • August 2005, pp. 502-506

ON A PROBLEM OF BROCARD

  • ALEXANDRU GICA (a1) and LAURENŢIU PANAITOPOL (a1)
  • DOI: http://dx.doi.org/10.1112/S0024609305004595
  • Published online: 01 August 2005
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.

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Bulletin of the London Mathematical Society
  • ISSN: 0024-6093
  • EISSN: 1469-2120
  • URL: /core/journals/bulletin-of-the-london-mathematical-society
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