Question 156
Let $\mathbb{Z}_+ = \{1, 2, 3, 4, \dots\}$ be the set of all positive integers. Determine all functions $f : \mathbb{Z}_+ \to \mathbb{Z}_+$ that satisfy
$f(mn) + 1 = f(m) + f(n)$ for all positive integers $m$ and $n$;
$f(2024) = 1;$
$f(n) = 1$ for all positive $n \equiv 22 \pmod{23}$.
$f(mn) + 1 = f(m) + f(n)$ for all positive integers $m$ and $n$;
$f(2024) = 1;$
$f(n) = 1$ for all positive $n \equiv 22 \pmod{23}$.