It is the fact?

Question

x^(n) = c^(2) - b^(2)
here for any x & n [except 2 & 2^(2)] we will always get two coprime squares "c" & "b" & "c" will always be odd.
From this prove that in FLT'S equation
A^(n) + B^(n) = C^(n)
if A & B are coprime then "C" has to be odd.

Answer 1

Hope I get a chance to see the answer when someone else provides it. Most interesting!

Answer 2

If b and c are not coprime then you can divide the common factor out, so you can asuume that c,band x are relative prime.

" A^(n) + B^(n) = C^(n)
if A & B are coprime then "C" has to be odd."

this statement is false. if a and b are coprime then their sum is even and thus C is not odd.