Takao Komatsu

collaborators

3 papers

math.CO2024

The Frobenius number for the triple of the 2-step star numbers

Takao Komatsu, Ritika Goel, Neha Gupta

In this paper, we give closed form expressions of the Frobenius number for the triple of the $2$ -step star numbers $an (n - 2) + 1$ for an integer $a \geq 4$ . These numbers have been…

math.NT2024

Frobenius numbers associated with Diophantine triples of $x^{2} + y^{2} = z^{r}$ (extended version)

Takao Komatsu, Neha Gupta, Manoj Upreti

We give an explicit formula for the $p$ -Frobenius number of triples associated with Diophantine equations $x^{2} + y^{2} = z^{r}$ , that is, the largest positive integer that can only be repr…

math.NT2023

Polynomial identities and Fermat quotients

Takao Komatsu, B. Sury

We prove some polynomial identities from which we deduce congruences modulo $p^{2}$ for the Fermat quotient $\frac{2 ^{p} - 2}{p}$ for any odd prime $p$ (Proposition 1 and Theorem 1). The…

The Frobenius number for the triple of the 2-step star numbers

Frobenius numbers associated with Diophantine triples of x2+y2=zr (extended version)

Polynomial identities and Fermat quotients

Frobenius numbers associated with Diophantine triples of $x^{2} + y^{2} = z^{r}$ (extended version)