diophantine or not?

Question

x^(n)=z^(2)-y^(2)
like 3^(3)=14^(2)-13^(2)
c^(n)-d^(n)=a^(2)-b^(2)
like 7^(3)-4^(3)=48^(2)-45^(2)
are these diophantine equations
in both the equations L.H.S is given.

Answer 1

x^(n)=z^(2)-y^(2) and c^(n)-d^(n)=a^(2)-b^(2)
are diophantine to me. I call them diophantic.
Th

Answer 2

although diophantine equations lack additional equations, they can be saved by trial and error.
you didn't post an actual problem dear... yet, i see you had three to four unknowns in your equations..
if you only have one equation to solve that kind of problem, then that's grossly diophantine...

[also, difference of two bases raised at positive powers can be simplified, like that of difference of two squares....]

Answer 3

dude, get a life