The Ramanujan-Alhena Singular Numbers Theorem

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This paper refutes the Lebesgue-Ramanujan-Nagell equation by reproducing counterexamples and extends the conjecture to identify other "singular numbers" like 28 that also yield five solutions.

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Abstract

The famous singularity of number 7; conjectured by Ramanujan from a Diofanthine equation. In which the answer is given in the subtraction of 2n for every number A greater than zero, at most two solutions were obtained except for number 7, in which case 5 solutions were obtained. What was analysed by many 20th century mathematicians such as Lebesgue, Nagell, Chowla, Lewis, Skolem, Apéry, among others. That, through their demonstrations, they supported this conjecture as true. It is currently known as the Lebesgue-Ramanujan-Nagell Equation. And to this day, contemporary mathematicians continue to study it. In this article, the equation was analysed and developed in such a way that several counterexamples were reproduced, which was good for its refutation. However, this was the starting point, which extended the conjecture from the unique case of the number 7 to several numbers in which 5 solutions were obtained such as the number 28 and which should also be defined as singular. Through what will be known as the Ramanujan-Alhena Singular Number Theorem

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last seen: 2026-05-20T01:45:00.602351+00:00