论文标题
自动求解由Ramanujan启发的立方二磷酸方程式
Automatic Solving of Cubic Diophantine Equations Inspired by Ramanujan
论文作者
论文摘要
在Ramanujan的《丢失的笔记本》中，有一个惊人的身份，可以为Cutic Fermat的最后一个定理提供无限的“几乎反例”，没有任何迹象表明他如何发现它。 1995年，迈克尔·赫希霍恩（Michael Hirschhorn）以一种出色的方式解释了拉玛努扬（Ramanujan）如何根据一定的多项式身份（共有四个立方体）做到这一点。更早的时间，埃里·贾博丁斯基（Eri Jabotinsky）在1946年发表的一篇文章（在《青少年的数学杂志》中）中解释了Ramanujan可能如何发现Hirschhorn方法所需的这些多项式身份。在这里，我们结合了这两个辉煌的想法（这可能是Ramanujan的做法），通过开发算法来求解大型立方双磷剂方程来自动化并概括它。在阅读艾米·阿尔茨瑙尔（Amy Alznauer）（b。安德鲁斯）令人愉快的孩子们的书《梦见无限的男孩》（Candlewick Press），2020年，我们对这个问题的兴趣重新点燃了，Ramanujan的身份出现在其中一个插图中。
In Ramanujan's Lost Notebook there is an amazing identity that furnishes infinitely many "almost counterexamples" to the cubic Fermat's Last Theorem, with no indication whatsoever how he discovered it. In 1995, Michael Hirschhorn explained, in a brilliant way, how Ramanujan may have done it, based on a certain polynomial identity for a sum of four cubes. Much earlier, Eri Jabotinsky, in an article published in 1946 (in a mathematics journal for teenagers) explained how Ramanujan may have discovered these polynomial identities needed for Hirschhorn's approach. Here we combine these two brilliant ideas (that may or may not have been how Ramanujan did it), automate it, and generalize, by developing an algorithm to solve a large class of cubic diophantine equations. Our interest in this problem was rekindled after reading Amy Alznauer's (b. Andrews) delightful children book "The Boy Who Dreamed of Infinity" (Candlewick Press), 2020, where Ramanujan's identity appears in one of the illustrations.
