Diophantine question.

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Hello, all!
    It is known that Fermat solved the Diophantine equation x^4 + y ^4
= z^2 over
the integers and proved that it has no nontrivial solutions. He used
the
method of infinite descent.
What can one say about the equation x^4 - y^4 = z^^2? Are there any
nontrivial
integer solutions? More generally, what is known about the equation
x^p - y^p = z^2, where p is an odd prime?
Regards,
Ray Steiner