An Introduction To Refined Neutrosophic Number Theory

Number theory is concerned with properties of integers and Diophantine equations. The objective of this paper is dedicated to introduce the basic concepts in refined neutrosophic number theory such as division, divisors, congruencies, and Pell's equation in the refined neutrosophic ring of integers Z(𝐼1 ,𝐼2). Also, algorithms to solve refined neutrosophic linear congruencies and refined neutrosophic Pell's equation will be presented and discussed