Diophantine equations are mathematical equations that seek integer solutions for a given set of variables. The term "Diophantine" is derived from the name of the ancient Greek mathematician Diophantus, who is considered the father of algebra. Synonyms for the term Diophantine equation include "integer equation," "integral equation," "Diophantus's problem," and "Diophantus's equation." Another term used to describe Diophantine equations is "indeterminate equations," referencing the fact that there are no restrictions placed on the variables involved. These equations have been studied for centuries and have a variety of applications in areas such as cryptography, number theory, and physics.