The Relatively Prime Nature of Consecutive Integers

# Nictor Mwamba1

1Department of Mathematics, The Copperbelt University, Kitwe, Zambia.

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.
Keywords: Consecutive integers, Relatively Prime, Greatest Common Divisor.

Cite this article as: Nictor Mwamba, The Relatively Prime Nature of Consecutive Integers, Int. J. Math. And Appl., vol. 10, no. 1, 2022, pp. 97-100.

References
1. ---, Art of Problems Solving, https://artofproblemsolving.com/wiki/index.php/Relativelyprime, Accessed March, (2022).
2. D. Saracino, Abstract Algebra a First Course, 2nd Edition, Waveland Press, (2008).
3. J. A. Gallian, Contemporary Abstract Algebra, 7th Edition, Richard Stratton, (2010).
4. T. W. Judson, Abstract Algebra Theory and Applications, (S.F.A.S.University Ed.), Stephen F. Austin State University, (2010).

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