Miraj's Numo: Generalized Algebraic Identity for the Sum and Difference of Powers

Abstract

This paper is concerned with the presentation of Miraj’s Numo: a research algebraic identity that converts the sums and differences of two nth powers into differences of squares. The method hinges on cleverly defining a parameter m that depends upon the ratio of the powers so that the transformation works for any two real numbers a, b, and any integer exponent n. We present a stepwise derivation, along with thorough cases, to show that Miraj’s Numo generalizes classic identities and contracts expressions to simpler forms. In the realm of mighty factors, the identity opens a new viewpoint to approach polynomial equations and factorization problems and may be of assistance in simplifying computations in higher algebra and number theory. With Miraj’s Numo in hand-that looks into hidden structures within power sums-there blossoms a path to- wards applications in such research areas as computational algebra, and even theoretical physics, where such algebraic manipulations find their needed application.