Question 99
By $\lfloor x \rfloor$ we denote the largest integer that is smaller or equal to $x$ and by $\lceil x \rceil$ we denote the smallest integer that is greater or equal to $x$.
For every given pair $(a, b)$ of positive natural numbers find all natural numbers $n$ with
$$
b + \lfloor \frac{n}{a} \rfloor = \lfloor \frac{n+b}{a} \rfloor.
$$
For every given pair $(a, b)$ of positive natural numbers find all natural numbers $n$ with
$$
b + \lfloor \frac{n}{a} \rfloor = \lfloor \frac{n+b}{a} \rfloor.
$$