Abstract

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.