Diophantine equations are equations for which solutions are restricted to a certain class of numbers, such as positive integers, negative integers, rational numbers, or some other criterion. They are named after, and were first investigated by, Diophantus. Diophantus was a Greek-educated Egyptian who lived in Alexandria sometime between 150 A.D. and 350 A.D.
There is a worksheet on Linear Diophantine Equations available on Math Lair.