University of Oulu

A simple solution to Archimedes’ cattle problem

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Author: Nygrén, Antti1
Organizations: 1University of Oulu, Faculty of Science, Department of Mathematical Sciences
Format: ebook
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1 MB)
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Language: English
Published: 2001
Publish Date: 2001-03-19


A simple solution to the classical Archimedes’ cattle problem is given. Unlike the previous ones, this is mainly based on elementary mathematics which, at least in principle, would have been available to the mathematicians of the classical era. The solution applies linear transformation and infinite descent in solving quadratic Diophantine equations in a manner which does not explicitly take advantage of continued fractions. The idea is to create a sequence of transformed equations, until an equation is obtained which can be solved easily. It turns out that this greatly simplifies the problem. The method of solving the Diophantine equations is especially suitable for a computer. The result can be easily used to produce several numerical solutions to the cattle problem.

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Series: Acta Universitatis Ouluensis. A, Scientiae rerum naturalium
ISSN-E: 1796-220X
ISBN: 951-42-5932-7
ISBN Print: 951-42-5931-9
Issue: 358
Copyright information: © University of Oulu, 2001. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited.