Show this truth?

Question

Show that in the equation
a^(n) - b^(n) = x^(n)
we have to always consider "a" as odd for a given "x" (odd or even) & "n" to make "a" & "b" coprime.

Answer 1

5^(2) - 3^(2) = 4^(2)

I think there is no n, which is greater than 2, satisfies the above equation.

Answer 2

Red is correct. If you change the equation a bit, by adding b^n to both sides, you get b^n + x^n = a^n

There are no integer solutions for this where n > 2.

This is from Fermat's last theorem :-)