An Investigation Into the Order of Integral Powers of Set of All Natural Numbers (London Journal of Research In Science: Natural and Formal, 2024)
This article established a fact on the order of difference of integral powers of all sets of natural numbers. The analysis was proof by use of established property of difference operator and principle of mathematical induction. The result proved conclusively that if the elements of an arithmetic progression of set of natural numbers with positive common difference are raised to positive power k, then the kth difference is equal to the product of the common difference raised to power k (dK) and k factorial (k!).
Keywords: Finite difference; mathematical induction; integral order; positive powers; arithmetic progression.