Number Theory

   

Introducing Pn Power Series in Number Theory: a Novel Way to Classify Natural Numbers

Authors: Pradeep Pant

Mathematics is a constantly evolving field where the search for new knowledge never stops. Discovering new mathematical series has been crucial for progress, leading to breakthroughs in many areas and offering fresh insights into the world of numbers. In this paper, we describe a new series called the Pn power series. The Pn power series is a superset of many series depending on the value of n. In number theory, we hypothesize a natural number X belongs to a power series Pn if its proper positive divisors (d1 , d2 , d3 ,. . . , X) follow; X^n = d1 * d2 * d3 *. . . * X (where n = 1, 1.5, 2, 2.5, 3, etc.). To illustrate this concept, 12 is a member of the P3 power series as its proper positive divisors, namely 1, 2, 3, 4, 6, and 12, satisfy the equation: 12^3= 1 * 2 * 3 * 4 * 6 * 12 = 1728. Similarly, 196 belongs to the P4.5 power series, with its divisors 1, 2, 4, 7, 14, 28, 49, 98, and 196,following the equation: 196^4.5 = 1 * 2 * 4 * 7 * 14 * 28 * 49 * 98 * 196 = 20,661,046,784. We believe that the implications of this observation are far-reaching, extending beyond number theory into various mathematical disciplines, and have the potential to open up new avenues of research and mathematical exploration.

Comments: 12 Pages. The supplementary file (Table S1) is available at https://bennettu-my.sharepoint.com/:x:/g/personal/pradeep_pant_bennett_edu_in/EcL2EjaiGNJFqyyLEo-SqqcBqEle9TZA32Wk3IAmC0Cy0A?e=LVosYs

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[v1] 2025-03-04 21:48:44

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