Affiliation:
1. Eastern Mediterranean University
2. Karabük University
Abstract
Abstract
Let \((F_{m})_{m\geq0}\) be the Fibonacci sequence defined by \(F_{0}=0, F_{1}=1\) and \(F_{m+2}=F_{m+1}+F_{m}\) for \(m\geq0.\) In this study, we investigate the solution of a Diophantine equations \(n!+d=F_{m}\) and in particular \(n!+3=F_{m}\) has only the unique positive solution \((n,m)=(2,5)\) which is a special form of the Brocard-Ramanujan equation.
MSC Classification: 11D04 , 11D09 , 11D75 , 11B75
Publisher
Research Square Platform LLC