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

TL;DR

This paper introduces a new method for finding solutions to the Brocard-Ramanujan Diophantine equation involving factorials and squares, aiming to identify all solutions or new ones.

Contribution

The paper proposes a novel approach to solve the Brocard-Ramanujan equation, advancing the understanding of its solutions.

Findings

Identified solutions for specific values of n

Developed a method to search for solutions systematically

Provided insights into the structure of solutions

Abstract

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