Tomohiro Yamada

activity

20232025

collaborators

6 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 $27 = 3^{3}$ .

math.NT2024

On Gauss-Kraitchik formula for cyclotomic polynomials via symmetric functions

Tomohiro Yamada

We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kraïtchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetri…

math.NT2023

Explicit improvements of the Brun-Titchmarsh theorem for arbitrary intervals

Tomohiro Yamada

We give an explicit version of Brun-Titchmarsh theorem applicable for arbitrary moduli and arbitrary intervals. For example, we show that $π(x+y; k, a)-π(x; k, a)<2y/(φ(k)(\log (y/…

math.NT2023

On a theorem of Kanold on odd perfect numbers

Tomohiro Yamada

We shall prove that if $N = p^{α} q_{1}^{2 β_{1}} q_{2}^{2 β_{2}} \dots q_{r - 1}^{2 β_{r - 1}}$ is an odd perfect number such that $p, q_{1}, \dots, q_{r - 1}$ are distinct primes, $p\equivα\equiv 1\mo…