Diophantus of Alexandria Arithmetica Diophantine equations Euclid
Very little is known about Diophantus of Alexandria; he probably lived in the third century AD, that is, about five hundred years after Euclid. Six out of the thirteen books of Diophantus's Arithmetica survive in the original Greek and four more survive in an Arabic translation. The Arithmetica is a collection of worked-out problems where the task is invariably to find rational solutions to a system of polynomial equations, usually of the form 



f
(
x
,
y
)
=

z

2




{\displaystyle f(x,y)=z^{2}}

 or 



f
(
x
,
y
,
z
)
=

w

2




{\displaystyle f(x,y,z)=w^{2}}

. Thus, nowadays, we speak of Diophantine equations when we speak of polynomial equations to which rational or integer solutions must be found.
