# Is an equation containing a factorial still called “Diophantine equation”?

Is an equation like $x^3+y^4=z!$ , $x,y,z\in\mathbb Z$ , $z\ge 0$ called "Diophantine equation" ?

I am not sure whether the only requirement is that the variables must be integers. Are factorials allowed, and what about something like $x^3+y^4=2^z$ ?

• @RobArthan I did not think otherwise, but some questions here deal with equations containing a factorial or a power like $2^z$ and they were called "diophantine", so I only wanted to clarify that. Thanks for your info. – Peter Apr 13 '17 at 22:49