Ramanujan-Nagell's Equation and Some of its Variations
Boudjem\^aa Anchouche
TL;DR
This paper explains Hasse's elementary proof of Ramanujan-Nagell's Theorem and explores natural extensions of the original equation, contributing to the understanding of its solutions and variations.
Contribution
It provides an accessible explanation of Hasse's proof and introduces new variations of Ramanujan-Nagell's equation.
Findings
Elementary explanation of Hasse's proof
Formulation of natural extensions of the equation
Potential insights into solutions of extended equations
Abstract
The paper consists of two parts. The aim of the first, and main, part is to explain, in an elementary way, Hasse's proof of Ramanujan-Nagell's Theorem. In the second part, we formulate some natural extensions of Ramanujan-Nagell's equation.
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Taxonomy
TopicsAdvanced Mathematical Identities · History and advancements in chemistry · History and Theory of Mathematics