The Brocard-Ramanujan's Diophantine Equation $n!+1=m^2$

S. Cerdá

The Brocard-Ramanujan's Diophantine Equation $n!+1=m^2$

Number Theory 2016-03-03 v5

Authors: S. Cerdá

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Abstract

In this paper we present a method to find the solutions to the Brocard-Ramanujan's problem $n! + 1 = m^2$ .

Keywords

Brocard-Ramanujan equation Diophantine equation integer solutions factorial perfect square number theory

Cite

@article{arxiv.1504.06694,
  title  = {The Brocard-Ramanujan's Diophantine Equation $n!+1=m^2$},
  author = {S. Cerdá},
  journal= {arXiv preprint arXiv:1504.06694},
  year   = {2016}
}

Comments

This paper is a new version of an old paper that was withdrawn by the author due to a logical fallacy detected by a reviewer. Now, this problem was solved using modular congruence techniques. There is a mistake at the solution

The Brocard-Ramanujan's Diophantine Equation $n!+1=m^2$

Abstract

Keywords

Cite

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