Foundations of Neutrosophic Number Theory

The aim of this paper is to establish a strong foundation of number theoretical concepts in the neutrosophic ring of integers 𝑍(𝐼). This work generalizes and deals with necessary and sufficient conditions for division, Euler's function, congruencies, and some other classical concepts in 𝑍(𝐼). The main result of this work is to show that Euler's famous theorem is still true in the case of neutrosophic integers. Also, this work introduces an algorithm to solve Pell's equation in the neutrosophic ring of integers Z(I).

Related Organizations

Tishreen University
Syrian Arab Republic

Keywords

Neutrosophic Euler's theorem, neutrosophic integers, neutrosophic congruence, neutrosophic Pell's equation

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average