MathNet 2024-part-02 — 168 problems (EN–VI) Question 47

Non-negative integers $a$, $b$, $q$, $r$ are all less than $5$ and satisfy conditions $q \lt a$ and $r \lt b \le a$. Dividing $qb + r$ by $5$ gives a remainder of $a$. Can we be certain that dividing $a$ by $b$ gives a remainder of $r$?