Some new equations concerning the Euler function

S. Tabirca and T. Tabirca
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 6, 2000, Number 2, Pages 34—38
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Authors and affiliations

S. Tabirca
Department of Computer Science, Transilvania University,
Brasov, Romania

T. Tabirca
Department of Computer Science – CNC,
University of Manchester, England

Abstract

This article presents some new equations concerning the Euler function. An equation for the sum \sum_{d|n} d^a \cdot \varphi^b(d) is found by using the multiplicative property. This is applied to find the sums \sum_{i=1}^n (i,n)^a and \sum_{i=1}^n i \cdot (i,n)^a.

References

  1. Hardy, G. H. and Wright, E. M. An Introduction to Number Theory, Calderon Press, Oxford, 1979.
  2. Lintes, I., Teoria Indicatorilor, Editura Universul, Bucuresti, 1944.
  3. Luca, F., On Some Functions of Tabirca, Octogon Mathematical Magazine, 6, 61-63, 1998.
  4. Rosen, K., Elementary Number Theory and its Application, Addison-Wesley, New York, 1993.
  5. Tabirca S. and Tabirca T. Two New Functions in Number Theory and some Applications for Smarandache Function, Libertas Mathematica, 18, 78-85.1998.

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Cite this paper

Tabirca, S. & Tabirca, T. (2000). Some new equations concerning the Euler function. Notes on Number Theory and Discrete Mathematics, 6(2), 34-38.

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