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arXiv · 1607.06366

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

Sanying Shi·Michel Weber
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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.

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Sanying Shi, Michel Weber. 2016-07-21. On the equation $ \boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets. https://arxiv.org/abs/1607.06366

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