The Greatest Common Divisors and The Least Common Multiples in Neutrosophic Integers

Authors : Yilmaz Çeven, Özlem Çetin

Pages : 411-416

Doi:10.19113/sdufenbed.1251290

View : 60 | Download : 70

Publication Date : 2023-12-25

Article Type : Research Paper

Abstract :As a continuation of previous studies, we give some results about the neutrosophic integers theory. We first stated that the neutrosophic real numbers are not closed according to the division operation. Later, we gave divisibility properties of neutrosophic integers. We have given properties such as the greatest common divisor for two neutrosophic integers being positive and unique. Then, we gave the Euclid’s Theorem, Bezout’s Theorem for neutrosophic ingers set Z[I]. It is known that these concepts are important for number theory in integers set Z. Finally, it is defined the least common multiple for neutrosophic integers. Finally, a theorem is given which enables one to easily find the least common multiple of neutrosophic integers and after a conclusion about the sign of the product of two neutrosophic integers, a theorem is given that shows the relationship of between the greatest common divisor with the least common multiple
Keywords : Nötrosfik tam sayılar, nötrosofik tamsayılarda en büyük ortak bölen, nötrosofik tam sayılarda en küçük ortak kat, nötrosofik tam sayılar için Euclid Algoritması, nötrosofik tam sayılar için Bezout Teoremi