AN INVESTIGATION INTO THE ORDER OF INTEGRAL PERFECT POWERS
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