What this shows?

Question

In fermats last theorem
a^(n) + b^(n) = c^(n)
i.e
[a^(n/2)]^2 + [b^(n/2)]^2 = [c^(n/2)]^2
if a^(n/2) , b^(n/2) & c^(n/2) exists then it is forming a rt. triangle also we know that any number having any power can be expressed as difference of two coprime perfect squares.
So [a^(n/2)]^2 , [b^(n/2)]^2 & [c^(n/2)]^2 are expressible as difference of two coprime perfect squares, so they will also make three rt. triangles.
Does this shows that Fermats last theorem is solvable by this concept?

Answer 1

Fermats last theorem is that there are no integer values for a, b and c which satisfy the equation when n is greater or equal to 3.

Your suggestion sticks to the case n=2 which is not part of the set up.