关于限制于因子闭集的方程$ \boldsymbol{n_1n_2=n_3n_4}$
On the equation $ \boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets
摘要：
研究了丢番图方程$n_1n_2=n_3n_4$的解的个数$N(B,F)$，其中$1\le n_1\le B$，$1\le n_3\le B$，$n_2, n_4\in F$和$F\subset [1,B]$是因子闭集.我们更特别地研究了当$F= \big\{m=p_1^{\e_1}\ldots p_k^{\e_k}, \e_j\in \{0,1\}, 1\le j\le k\big\}$、$p_1,\ldots,p_k$是不同素数时的情况。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
