A simple solution to Archimedes' cattle problem (Q2713284)

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