Takao Komatsu

collaborators

Showing math.NTShow all

2 papers · 1 filter

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…

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)