arXiv subjects

D. Sadornil

Publications and source records attributed to D. Sadornil.

3 recordsLinked to original sources

arXiv2021

On $μ$-Sondow Numbers

Given an integer $μ$, we study the numbers that satisfy the condition $\fracμ{n} + \sum_ {p \mid n} \frac {1} {p} \in \mathbb{N}$. This condition, which is reminiscent of the one satisfied by Giuga numbers ($μ=-1$), also includes the so-called \cite{sondow} weak primary pseudoperfect numbers ($μ=1$). As a tribute to our late colleague Jonathan Sondow (1943 -- 2020), we have named these numbers $ μ$-Sondow numbers. In this paper, we give several different characterizations of these numbers, all of them suggested by well-known characterizations of the Giuga numbers. We also relate these numbers to the well-known Erdös-Moser equation and we present some conjectures about them.

math.NT↗

arXiv2006

A note on factorisation of division polynomials

In the paper Factorisation of division polynomials (H. Verdure, Proc. japan Academy, Ser A. 80 n. 5), Verdure gives the factorisation patterns of division polynomials of elliptic curves defined over a finite field. However, the result given there contains a mistake. In this paper, we correct it.

math.NT↗

arXiv2005

Elliptic curves with rational subgroups of order three

In this article we present a characterization of elliptic curves defined over a finite field Fq which possess a rational subgroup of order three. There are two posible cases depending on the rationality of the points in these groups. We show that for finite fields Fq, q= -1 mod 3, all elliptic curves with a point of order 3, they have another rational subgroup whose points are not defined over the finite field. If q = 1 mod 3, this is no true; but there exits a one to one correspondence between curves with points of order 3 and curves with rational subgroups whose points are not rational.

math.NT↗