The Miraj’s Numo: Generalized Algebraic Identity for the Sum and Difference of Powers
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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 towards applications in such research areas as computational algebra, and even theoretical physics, where such algebraic manipulations find their needed application.
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Pathak M. MIRAJS CUBO: A comprehensive exploration of relation of cubic identities with square numbers. Int J Adv Res. 2025;20–23. Available from: https://www.journalijar.com
Hardy GH. A course of pure mathematics. Cambridge: Cambridge University Press; 1908.
Hardy GH, Wright EM. An introduction to the theory of numbers. Oxford: Oxford University Press; 2008.
Geddes K, Czapor SR, Labahn GE. Algorithms for computer algebra. New York: Springer; 1992.
Ogata K. Modern control engineering. Prentice Hall; 2010.