Malaysian Journal of Mathematical Sciences, January 2020, Vol. 14, No. 1
Nonclassical Study on certain Diophantine Inequalities involving Multiplicative Arithmetic Functions
Said Boudaoud, Djamel Bellaouar, and Abdelmadjid Boudaoud
Corresponding Email: bellaouar.djamel@univ-guelma.dz
Received date: 28 April 2018
Accepted date: 29 December 2019
Abstract:
This paper, for the most part, is in the framework of Internal Set Theory (IST), where any real number must be infinitesimal, appreciable or unlimited; these numbers are called standard or nonstandard. In particular, any positive integer must be standard (limited) or nonstandard (unlimited). In the first part, we estimate for an unlimited positive integer \(n\) and to an infinitesimal near, the values of some arithmetic functions of the form \(\frac{f(n)}{g(n)}\), where \(f\) and \(g\) are constructed using multiplicative functions. Further, in classical mathematics, several Diophantine inequalities involving certain multiplicative arithmetic functions are studied.
Keywords: Diophantine Inequalities, Multiplicative Functions, Prime Numbers, Internal Set Theory
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