Positive Rational Solutions to X : a Number-theoretic Excursion
نویسنده
چکیده
Late in the last millennium, the second author ran a seminar course for undergraduates which was intended to introduce them to problem-solving and questionasking in the context of mathematical research. He led them through the classic “difficult” equation x = y, x, y > 0, (1) whose solution is much easier than one would think at first glance. Solutions were sought, first over R, then over Z and finally over Q. In the context of this seminar, it was natural to consider the variant equation x = y, x, y > 0, (2) which does not seem to have appeared in the literature. It turns out that there are solutions to (2) which do not fit the well-known parametric pattern of (1); c.f. (5) below. For example,
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Positive Rational Solutions to xy = ymx: A Number-Theoretic Excursion
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تاریخ انتشار 2008