Order of Integral Perfect Powers: A Mathematical Approach

Authors

  • Ladan Umaru Ibrahim Department of Mathematics, University of Jos, P.M.B. 2084, Jos, Plateau State, Nigeria.
  • Ukwu Chukwunenye Department of Mathematics, University of Jos, P.M.B. 2084, Jos, Plateau State, Nigeria.
  • Apine Elijah Department of Mathematics, University of Jos, P.M.B. 2084, Jos, Plateau State, Nigeria.

DOI:

https://doi.org/10.9734/bpi/rhmcs/v2/7555F

Keywords:

Finite difference, mathematical induction, integral order, positive powers, reproductive property

Abstract

This article obtained the structure of all orders of differences of integral perfect powers with explicitly determined computational dispositions. The proofs were achieved by deft deployment of combinatorial techniques, established reproductive property of the difference operator and mathematical induction principle. The results proved conclusively that if any number of consecutive integers are raised to a positive integral power k, then the Kth difference is equal to k!

Published

2022-10-31

How to Cite

Ladan Umaru Ibrahim, Ukwu Chukwunenye, & Apine Elijah. (2022). Order of Integral Perfect Powers: A Mathematical Approach. Research Highlights in Mathematics and Computer Science Vol. 2, 1–10. https://doi.org/10.9734/bpi/rhmcs/v2/7555F

Issue

Research Highlights in Mathematics and Computer Science Vol. 2

Section

Chapters