Discussions: A Cubic Equation of Newton's
About: This article is published in American Mathematical Monthly.The article was published on 1926-04-01. It has received 2 citations till now. The article focuses on the topics: Cubic function.
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TL;DR: A direct algebraic method is used that yields all rational solutions of Newton’s equation, albeit parameterized in a way very different from that obtained by Barnett (and Hajja), and an explicit, nonobvious, birational correspondence between the two parameterizations is established.
Abstract: A Newton quadrilateral is a convex quadrilateral inscribed in a circle, with one side a diameter. For diameter d and the other side lengths a,b, and c , Newton arrived at the cubic equation d3−(a2+...
3 citations
Cites background from "Discussions: A Cubic Equation of Ne..."
...Anning discussed Newton’s equation in a short note in [6]....
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01 Jan 2015
TL;DR: In this article, the second component of a solution (u, v) is a perfect square, and the problem of finding a solution with a constant number of perfect squares is studied.
Abstract: An interesting problem concerning the Pell’s equation \(u^{2} - Dv^{2} = 1\) is to study when the second component of a solution (u, v) is a perfect square.