what is the relation?

Question

a^(n)-b^(n)
=(a-b)^(n)+nk(a-b)
here what is the relation between this equation where "a" is odd ,"b' is any natural number and "n" is a prime or its factors are the same primes(except multiples of 5 but 5 is included) and & the fermats last theorem.here k will always be a natural number.

Answer 1

First of all this statement is false.
take
n=2 ( this is a prime )
a=1 ( a is odd )
b=1

then K can be anything including rationals.

I do not see any relation between fermat except that the operator ^n is used.

Fermat cant be proved by only using some algebraic identities.