Diophantine Equations
Diophantine Equations
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DOI：
10.1007/3-540-26598-8_7
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发表时间：
2008-05
期刊：
影响因子：
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通讯作者：
Gove Effinger;G. Mullen
中科院分区：
文献类型：
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作者：
Gove Effinger;G. Mullen
丢番图方程，即整数系数方程的整数解决方案的要求，是最古老的数学科目之一。早期的历史事件经常以谜题的形式出现，也许正是因为这个原因，丢番图方程在我们的数学教育中基本上被忽视了。然而，具有讽刺意味的是，丢番图方程在现代应用中发挥着越来越重要的作用，更不用说一些丢番图问题，特别是那些无法解决的问题，已经激发了大量的数学思维，以很少有其他刺激的方式推进了数论的主题。在这里，我们将处理一些基本的事实和规则，并了解三角形和毕达哥拉斯数，费马大定理，一个未解决的猜想哥德巴赫，另一个猜想欧拉一个被驳斥，虽然它看起来相当令人信服，而它持续。
Diophantine equations, ie, equations with integer coefficients for which integer solutions are sought, are among the oldest subjects in mathematics. Early historical occurrences often appeared in the guise of puzzles, and perhaps for that reason, Diophantine equations have been largely neglected in our mathematical schooling. Ironically, though, Diophantine equations play an ever-increasing role in modern applications, not to mention the fact that some Diophantine problems, especially the unsolvable ones, have stimulated an enormous amount of mathematical thinking, advancing the subject of number theory in a way that few other stimuli have. Here we shall deal with some of the basic facts and rules and get to know triangular and Pythagorean numbers, Fermat’s Last Theorem, an unsolved conjecture by Goldbach, and another conjecture by Euler–one that was refuted, although it looked quite convincing while it lasted.