Let N be the set of positive integers. Find all functions f:N->N that satisfy the equation

f^abc-a(abc) + f^abc-b(abc) + f^abc-c(abc) = a + b + c

for all a, b, c ≥ 2.

(Here f¹(n) = f(n) and f^k(n) = f(f^k-1(n)) for every integer k greater than 1)
(Also note: abc is the product a·b·c and not the concatenation 100a+10b+c)