A note on Euler’s totient function

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 32–35
DOI: 10.7546/nntdm.2019.25.1.32-35
Full paper (PDF, 157 Kb)

Details

Authors and affiliations

József Sándor
Department of Mathematics, Babes-Bolyai University
Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania

Abstract

In this paper, we give three identities involving the Lucas sequences of the first kind and of the second kind in order to obtain infinite families of solutions to some Diophantine equations. Some of these families are new and the others are larger than those known until now.

Keywords

• Euler’s totient
• Primes
• Fermat’s little theorem
• Quadratic residues

2010 Mathematics Subject Classification

• 11A07
• 11A25
• 11N37

References

1. Hardy, G. H. & Wright, E. N. (1964). An Introduction to the Theory of Numbers, Oxford University Press.
2. Sándor, J. (1989). On the composition of some arithmetic functions, I. Studia Univ. Babeş-Bolyai, Math., 34, 7–14.
3. Sándor, J. (2005). On the composition of some arithmetic functions, II. J. Ineq. Pure Appl. Math., 6 (2), Article No. 73.
4. Sándor, J. (2005). On the composition of some arithmetic functions, III. (unpublished manuscript).
5. Sándor, J. & Crstici, B. (2004). Handbook of Number Theory II, Springer.