On the equation $ \boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets

Sanying Shi; Michel Weber

On the equation $ \boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets

Number Theory 2018-10-02 v3

Authors: Sanying Shi , Michel Weber

Abstract

We study the number of solutions $N(B,F)$ of the diophantine equation $n_1n_2=n_3n_4$ , where $1\le n_1\le B$ , $1\le n_3\le B$ , $n_2, n_4\in F$ and $F\subset [1,B]$ is a factor closed set. We study more particularly the case when $F= \big\{m=p_1^{\e_1}\ldots p_k^{\e_k}, \e_j\in \{0,1\}, 1\le j\le k\big\}$ , $p_1,\ldots,p_k$ being distinct prime numbers.

Keywords

diophantine equation factor closed set number of solutions prime numbers

Cite

@article{arxiv.1607.06366,
  title  = {On the equation $ \boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets},
  author = {Sanying Shi and Michel Weber},
  journal= {arXiv preprint arXiv:1607.06366},
  year   = {2018}
}

Comments

This revised and corrected version has been published in Acta Math. Sinica , 2018 , vol. 34 No. 10, pp. 1517--1530

On the equation $ \boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets

Abstract

Keywords

Cite

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