• Onthe factorization of two adjacent numbers in multiplicatively closed sets generated by two elements

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0037

• # Keywords

Multiplicatively closed sets; continued fractions; primary and secondary convergents

• # Abstract

For two natural numbers $1$ < $p1$ < $p2$, with $\alpha = \frac{log(p1)} {log(p2)}$ irrational, we describe in the Main Theorem $\Omega$ and in Note 1.5, the factorization of two adjacent numbers in the multiplicatively closed subset $S = \{p^{i}_{1} p^{j}_{2}\,|\, i, j \in \mathbb{N}\cup\{0\}\}$ using primary and secondary convergents of $\alpha$. This suggests the general Question 1.2 for more than two generators which is still open.

• # Author Affiliations

1. No. 104, Bldg 23, Lakshmi Paradise, 5th Main, 11th Cross, LN Puram, Bengaluru 560 021, India

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019