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Diophantine Equations Involving Arithmetic Functions of Factorials

Baczkowski, Daniel M.

Abstract Details

2004, Master of Arts, Miami University, Mathematics.

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 φ or σ (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 ρ is prime and k>0 , then

φ(n!)=ρ k m! and ρ k f(n!)=m!

have finitely many solutions (ρ,k,m,n) , too.

Reza Akhtar (Advisor)
24 p.

Recommended Citations

Citations

  • Baczkowski, D. M. (2004). Diophantine Equations Involving Arithmetic Functions of Factorials [Master's thesis, Miami University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=miami1088086258

    APA Style (7th edition)

  • Baczkowski, Daniel. Diophantine Equations Involving Arithmetic Functions of Factorials. 2004. Miami University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=miami1088086258.

    MLA Style (8th edition)

  • Baczkowski, Daniel. "Diophantine Equations Involving Arithmetic Functions of Factorials." Master's thesis, Miami University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=miami1088086258

    Chicago Manual of Style (17th edition)