AN INVESTIGATION INTO THE ORDER OF INTEGRAL PERFECT POWERS

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Published: 2015-12-03

Page: 12-18


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.

*Author to whom correspondence should be addressed.


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 !

Keywords: Finite difference, mathematical induction;, integral order, positive powers, reproductive property


How to Cite

IBRAHIM, L. U., CHUKWUNENYE, U., & ELIJAH, A. (2015). AN INVESTIGATION INTO THE ORDER OF INTEGRAL PERFECT POWERS. Asian Journal of Mathematics and Computer Research, 10(1), 12–18. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/228

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