Question 145
Determine all integers $n \ge 1$ for which there exists at least one pair of positive integers $(a, b)$ such that:
(i) The integer $a^2 + b + 3$ is not divisible by the cube of a prime number.
(ii) $\frac{ab+3b+8}{a^2+b+3} = n$
(i) The integer $a^2 + b + 3$ is not divisible by the cube of a prime number.
(ii) $\frac{ab+3b+8}{a^2+b+3} = n$