Number Theory

    

On a Variant of Brocard's Problem Via the Diagonalization Method

Authors: Theophilus Agama

In this paper we introduce and develop the method of diagonalization of functions $f:mathbb{N}longrightarrow mathbb{R}$. We apply this method to show that the equations of the form $Gamma_r(n)+k=m^2$ has a finite number of solutions $nin mathbb{N}$ with $n>r$ for any fixed $k,rin mathbb{N}$, where $Gamma_r(n)=n(n-1)cdots (n-r)$ denotes the $r^{th}$ truncated Gamma function.

Comments: 6 Pages. The requirements in the diagonal method has been greatly simplified

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Submission history

[v1] 2022-05-20 21:59:37
[v2] 2023-01-13 13:02:00

Unique-IP document downloads: 263 times

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