Editing Equation (section)

===Diophantine equations===
{{main|Diophantine equation}}
A Diophantine equation is a [[polynomial equation]] in two or more unknowns for which only the [[integer]] [[Zero of a function#Polynomial roots|solutions]] are sought (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantine equation is an equation between two sums of [[monomials]] of [[Degree of a polynomial|degree]] zero or one. An example of linear Diophantine equation is {{math|''ax'' + ''by'' {{=}} ''c''}} where ''a'', ''b'', and ''c'' are constants. An exponential Diophantine equation is one for which exponents of the terms of the equation can be unknowns.

Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an [[algebraic curve]], [[algebraic surface]], or more general object, and ask about the [[lattice point]]s on it.

The word ''Diophantine'' refers to the [[Greek mathematics#Hellenistic|Hellenistic mathematician]] of the 3rd century, [[Diophantus]] of [[Alexandria]], who made a study of such equations and was one of the first mathematicians to introduce [[Mathematical symbol|symbolism]] into [[algebra]]. The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis.