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arXiv · 1806.03344

On the Factorization of Two Adjacent Numbers in Multiplicatively Closed Sets Generated by Two Elements

C. P. Anil Kumar
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Abstract

For two natural numbers $1<p_1<p_2$, with $\alpha = \frac{\log(p_1)}{\log(p_2)}$ irrational, we describe, in main Theorem $\Omega$ and in Note $1.5$, the factorization of two adjacent numbers in the multiplicatively closed subset $S = \{p_1^ip_2^j\mid i,j\in \mathbb{N}\cup\{0\}\}$ using primary and secondary convergents of $\alpha$. This suggests general Question $1.2$ for more than two generators which is still open.

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C. P. Anil Kumar. 2018-06-02. On the Factorization of Two Adjacent Numbers in Multiplicatively Closed Sets Generated by Two Elements. https://doi.org/10.1007/s12044-020-00566-8

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