Question 131
Determine all integers $n \geq 1$ for which there exists a pair $(a, b)$ of positive integers with the following properties:
i) No cube of a prime divides $a^{2}+b+3$.
ii) $\frac{a b+3 b+8}{a^{2}+b+3}=n$.
i) No cube of a prime divides $a^{2}+b+3$.
ii) $\frac{a b+3 b+8}{a^{2}+b+3}=n$.