On Systems of Linear Diophantine Equations
On Systems of Linear Diophantine Equations
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线性丢番图方程组
DOI：
10.1080/0025570x.1996.11996448
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发表时间：
1996
影响因子：
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通讯作者：
F. Lazebnik
中科院分区：
文献类型：
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作者：
F. Lazebnik
我敢打赌，很多读过这封信的人最近都遇到了一些事情。教一个新的题目，你看不懂其中的一个证明。您第一次尝试填补空白的尝试失败了。你翻阅你的账本，寻找答案。接下来，你问同事，去图书馆，甚至可以使用馆际互借。一切都是徒劳的。然后，你会突然发现，事实上，你无法回答一个更基本、更有趣的问题。你再看一遍书。他们似乎有成千上万个奇怪的问题的答案，但对你的(最自然的一个！)却没有答案。与此同时，你不能相信你的问题会被一代又一代的数学家忽视。日子一天天过去，痛苦仍在继续。然后有一天，以某种方式，你找到了答案。在我的案例中，答案就在我已经拥有的一本书中。它来自一个我很久以前就知道的定理，但我从来没有想过这个特殊的应用。事实上，我必须承认，这个定理几乎出现在我检查过的每一本书中，但从来没有指向这个特定应用的指针，即使是作为练习。作者是不是不知道这个应用程序？或者，提到这件事似乎是显而易见的？无论如何，故事是这样的。
Introduction Something happened to me recently I would wager has happened to many who read this note. Teaching a new topic, you cannot understand one of the proofs. Your first attempt to fill the gap fails. You look through your books for an answer. Next, you ask colleagues, go to the library, maybe even use the interlibrary loan. All in vain. Then it strikes you that, in fact, you cannot answer an even more basic and seemingly more interesting question. You peruse the books again. They seem to have answers to thousands of strange questions, but not to yours (the most natural one!). At the same time you cannot believe that your question could have been overlooked by generations of mathematicians. Days pass; the agony continues. Then one day, some way or other, you find the answer. In my case the answer was in a book I already owned. It followed from a theorem I had known for a long time, but I had never thought of this particular application. I must admit, indeed, that this theorem appeared in almost every book I had checked, but never with a pointer to this particular application, even as an exercise. Were the authors unaware of the application? Or did it seem to obvious to mention? In any case, here is the story.