# Diophantine Equations Involving Arithmetic Functions of Factorials

Abstract (Summary)

We examine and classify the solutions to certain Diophantine equations involving factorials and some well known arithmetic functions. F. Luca has showed that there are finitely many solutions to the equation: f(n!)=a m! where f is one of the arithmetic functions ? or ? (sum of the divisors function) and a is a rational number. We study the solutions for this equation when a is a prime power or a reciprocal of a prime power. Furthermore, we prove that if ? is prime and k>0 , then ?(n!)=? k m! and ? k f(n!)=m! have finitely many solutions (?,k,m,n) , too.
Bibliographical Information:

Advisor:

School:Miami University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:math mathematics factorial arithmetic diophantine n m

ISBN:

Date of Publication:01/01/2004