There are two simplified forms for these equations:

Consider Fermat's Last Theorem Equation as follows:

Therefore:

For odd p

For even p

Where:

andSome of the equations:

p=2

p=3

p=4

p=5

Maybe it could offer an alternative proof for Fermat's Last Theorem. I had tried rational root theorem and substitution of solution of these forms:

orStill got stumbled upon few steps. Maybe Galois theory might be used to explain why

can never be rational in the form of root w and variable s.]]>