A note on a problem of Brocard-Ramanujan

C. Helou; L. Haddad

doi:10.1007/s11139-008-9139-8

A note on a problem of Brocard-Ramanujan

C. Helou
, L. Haddad

Penn State Brandywine

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	155-161
Number of pages	7
Journal	Ramanujan Journal
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s11139-008-9139-8
State	Published - Nov 2008

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-008-9139-8

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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.",

author = "C. Helou and L. Haddad",

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AU - Haddad, L.

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AB - 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.

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UR - https://www.scopus.com/pages/publications/54849441203#tab=citedBy

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DO - 10.1007/s11139-008-9139-8

M3 - Article

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EP - 161

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JF - Ramanujan Journal

IS - 2

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A note on a problem of Brocard-Ramanujan

Abstract

All Science Journal Classification (ASJC) codes

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