An Investigation into the Order of Integral Powers of Consecutive Elements of Set of Even and odd Numbers

Abstract

This article analysed the order of difference of integral perfect powers of the set of even and odd numbers. The analysis was proof by the use of combinatorial terminologies, established property of the difference operator and the principle of mathematical induction. The results proved conclusively that “if any number of consecutive odd or even integers are raised to a positive power k, then the kth difference is equal to 2^kk!