On an Inequality Related to the Legendre Totient Function

Volume 3, Issue 3, 2002

Article 37

ON AN INEQUALITY RELATED TO THE LEGENDRE TOTIENT FUNCTION

DEPARTMENT OF MATHEMATICS, STATISTICS AND PHILOSOPHY
FIN-33014 UNIVERSITY OF TAMPERE,
FINLAND
E-Mail: mapehau@uta.fi

Received 06 February, 2002; Accepted 27 February, 2002.
Communicated by: J. Sandor

ABSTRACT.

Let $\Delta(x, n)=\varphi(x, n)-x\varphi(n)/n$ , where $\varphi(x, n)$ is the Legendre totient function and $\varphi(n)$ is the Euler totient function. An inequality for $\Delta(x, n)$ is known. In this paper we give a unitary analogue of this inequality, and more generally we give this inequality in the setting of regular convolutions.

Key words:
Legendre totient function, Inequality, Regular convolution, Unitary convolution.

2000 Mathematics Subject Classification:
11A25.

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