Yet to be proved?

Question

It is impossible to write
2^(n) = t^(n) - w^(n)
for n>1 having natural solutions for "t" & "w".
Prove it with guts.

Answer 1

it has already been proved for n > 2.

2^n = t^n - w^n => t^n = 2^n + w^n

Famous Format's Last theorem

It need to be proved for 2

4= t^2-w^2
or (t-w)*(t+w) = 4

t-w and t+w have to be both odd or both even

only solution = t-w = t+w = 2 or w = 0
so no solution