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