A Little Generalization Of Fermat's Little Theorem

I just whipped this out today. But I am unsure it is actually true. Is
it?

Let m be an integer >=2.

Let n be any positive integer (possibly composite).

Then m^n - m =

sum{p|n} p*j(p),

where the sum is over the distinct primes dividing n, and each j(p) is
some integer >= m*b(p),

where b(p) is the exponent raising the prime p in the prime-
factorization of n.

Thanks,
Leroy Quet

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