关于出租车号码的搜索
On Hunting for Taxicab Numbers
摘要：
本文利用一些已知的方法研究了表示为两个相等的奇次幂和的数的一些性质，等式$x^n+y^n=N$用于$n\ge3$。它起源于开发搜索新出租车号码的算法（即，可以用许多不同的方式表示为正立方体之和的自然数），并验证它们的极小性。我们讨论的丢番图方程，可用于我们的调查性质。该技术被应用于开发一种算法，该算法允许我们计算新的出租车号码（即，以$k$不同方式表示为两个正立方之和的数字），用于$k=7...14$。
英文摘要：
In this article, we make use of some known method to investigate some properties of the numbers represented as sums of two equal odd powers, i.e., the equation $x^n+y^n=N$ for $n\ge3$. It was originated in developing algorithms to search new taxicab numbers (i.e., naturals that can be represented as a sum of positive cubes in many different ways) and to verify their minimality. We discuss properties of diophantine equations that can be used for our investigations. This techniques is applied to develop an algorithm allowing us to compute new taxicab numbers (i.e., numbers represented as sums of two positive cubes in $k$ different ways), for $k=7...14$.
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。
