An Investigation into the Order of Difference of Product of Consecutive Integral Perfect Powers
Ladan, Umaru Ibrahim *
Department of Computer Science, Faculty of Natural Sciences, University of Jos, Nigeria.
Emmanuel, J. D. Garba
Department of Mathematics, Faculty of Natural Sciences, University of Jos, Nigeria.
Tanko Ishaya
Department of Computer Science, University of Jos, Plateau State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The article established an analysis on the difference of the product of order of integral perfect powers. The proof on the analysis were achieved by the use of property of difference operator, combinatorial technique, mathematical induction principle. The results proved conclusively that if any number of consecutive integers are raised to a positive power k, then the (2k)th difference of the product of the kth power of two consecutive integers is equal to (2k)!
Keywords: Mathematical induction, finite difference, positive powers, integral order, factorial differential operator