Introduction to Diophantine Equations

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Diophantine equation – an equation whose roots are required to be integers. In this article we will only touch on a few tiny parts of the field of linear Diophantine equations. Some of the tools introduced, however, will be useful in many other parts of the subject. Suppose that dolls sell for $7 each, and toy train sets sell for $18. A store sells 25 total dolls and train sets, and the total amount received is $208. How many of each were sold? Easy, two equations and two unknowns. However what if the problem was changed to: Suppose a store sells only dolls and train sets, and the total amount received is $208. How many of each were sold? One equation with two unknowns….