Tomohiro Yamada

collaborators

3 papers

math.NT2025

On the Ratat-Goormaghtigh equation and integer points close to the graph of a smooth function

Tomohiro Yamada

We prove that the sum of reciprocals $1/ x$ of integer solutions of $(x^{m} - 1) / (x - 1) = N$ with $x, m \geq 2$ for a given integer $N$ except the smallest $x$ is smaller than $5.9037$ . If…

math.NT2025

Ratios of two powers of van der Laan-Padovan numbers

Tomohiro Yamada

The van der Laan-Padovan sequence $P_{n} (n = 0, 1, \dots)$ is defined by $P_{0} = 1, P_{1} = P_{2} = 0$ , and $P_{n + 3} = P_{n + 1} + P_{n}$ for $n = 0, 1, \dots$ . We determine all pairs $(P_{m}, P_{n})$ sat…

math.NT2024

Determining all biunitary triperfect numbers of a certain form

Tomohiro Yamada

We shall show that $2160$ is the only biunitary triperfect number divisible by $27 = 3^{3}$ .