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arXiv 1701.02604math.NT
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关于丢番图方程$ \sum_{i=1}^n a_ix_{i} ^6+\sum_{i=1}^m b_iy_{i} ^3= \sum_{i=1}^na_iX_{i}^6\pm\sum_{i=1}^m b_iY_{i} ^3 $

On the Diophantine equations $ \sum_{i=1}^n a_ix_{i} ^6+\sum_{i=1}^m b_iy_{i} ^3= \sum_{i=1}^na_iX_{i}^6\pm\sum_{i=1}^m b_iY_{i} ^3 $

Farzali Izadi, Mehdi Baghalagdam

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9 pages
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摘要：

本文利用椭圆曲线理论求解丢番图方程$\sum_{i=1}^n a_ix_{i} ^6+\sum_{i=1}^m b_iy_{i} ^3= \sum_{i=1}^na_iX_{i}^6\pm\sum_{i=1}^m b_iY_{i} ^3$，其中$n$，$m$ $\geq 1$和$a_i$，$b_i$为任意非零整数.对于任意整数$n$，$m$，$a_i$和$b_i$，我们可以找到丢番图方程的无穷多个非平凡正解，也可以得到无穷多个非平凡参数解.

英文摘要：

In this paper, the elliptic curves theory is used for solving the Diophantine equations $\sum_{i=1}^n a_ix_{i} ^6+\sum_{i=1}^m b_iy_{i} ^3= \sum_{i=1}^na_iX_{i}^6\pm\sum_{i=1}^m b_iY_{i} ^3$, where $n$, $m$ $\geq 1$ and $a_i$, $b_i$, are fixed arbitrary nonzero integers. By our method, we may find infinitely many nontrivial positive solutions and also obtain infinitely many nontrivial parametric solutions for the Diophantine equations for every arbitrary integers $n$, $m$, $a_i$ and $b_i$.

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。

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