Question 27
The non-negative integers $a$, $b$, $c$ are such that the numbers
$$
m = \frac{5a + 6b + 7c + 6}{4a + 3b + 2c + 3} \quad \text{and} \quad n = \frac{a + 2b + 3c + 5}{3a + b + 2c + 5}
$$
are both integers.
a. Prove that $m \ge 2$.
b. Find $m$ and $n$.
$$
m = \frac{5a + 6b + 7c + 6}{4a + 3b + 2c + 3} \quad \text{and} \quad n = \frac{a + 2b + 3c + 5}{3a + b + 2c + 5}
$$
are both integers.
a. Prove that $m \ge 2$.
b. Find $m$ and $n$.