The Relatively Prime Nature of Consecutive Integers


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Authors

  • Nictor Mwamba Department of Mathematics, The Copperbelt University, Kitwe, Zambia.

Keywords:

Consecutive integers, Relatively Prime, Greatest Common Divisor

Abstract

The purpose of this article is to demonstrate that consecutive integers are relatively prime and that the converse is true for a special case. This paper introduces two methods/proofs of showing this. Firstly, a proof that depends on the Division Algorithm, Euclidean Algorithm, and Bezout's Lemma has been discussed. The uniqueness of this proof is its dependence of on other theorems. It can be thought to be an application of the aforementioned algorithms and lemma. In this article, the postulate that consecutive integers are relatively prime has been referred to as The Relative Prime Nature of Consecutive Integers. Secondly, a proof by mathematical induction has been also used to show that two consecutive integers are relatively prime. Since mathematical induction is only applicable when working with positive integers, this proof applies only to positive integers.

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Published

02-04-2022

How to Cite

Nictor Mwamba. (2022). The Relatively Prime Nature of Consecutive Integers. International Journal of Mathematics And Its Applications, 10(1), 97–100. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/18

Issue

Section

Research Article