(a^(n)b - ab^(n))/(2n)

When a and b are integers, and when the result is an integer too, i predict n is a prime number.

How can I prove it?

EDIT:

a and b mustn’t be equal to n and n mustn’t be 2.

"(a^(n)b - ab^(n))/(2n)

When a and b are integers, and when the result is an integer too, i predict n is a prime number."

Hmmm!

a = 4, b = 2, n = 4 gives (a^{n}b - ab^{n})/(2n) = 56

a, b and (a^{n}b - ab^{n})/(2n) are all integers, but n isn't prime.

Indeed

Then

a and b must not be equal to n.

You’ll need tighter constraints than that!

With a = 4, b = 2, n = 8, the result is 8128. n still not prime.