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)

Suppose that the function G is a solution to the problem. Then so is the function G*, where G*(k) = G(k) whenever k is the product of at least three (possibly duplicate) primes and G*(k) takes on any arbitrary value when k is a prime or a product of two primes.

Edited on August 16, 2021, 9:56 pm

Posted by FrankM on 2021-08-16 21:56:11