A note on a problem of Brocard-Ramanujan

C. Helou, L. Haddad

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The Brocard-Ramanujan problem pertains to the Diophantine equation n!+1=m2. Using the quadratic reciprocity law, we prove the existence of many infinite families of positive integers n such that n!+1 is not a perfect square, and we give several simple criteria for n!+1 to be a non-square.

Original languageEnglish (US)
Pages (from-to)155-161
Number of pages7
JournalRamanujan Journal
Volume17
Issue number2
DOIs
StatePublished - Nov 1 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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