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

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    • 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
    • Dates

  • Proceedings – Mathematical Sciences | News

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