Question 98
(a) Find all pairs $(m, n)$ of nonnegative integers that satisfy the equation
$$
5 m + 8 n = 120
$$
(b) Let $a$, $b$ and $c$ be positive integers with $c \gt 1$ such that
$$
\frac{1}{a} + \frac{1}{b} = \frac{1}{c}
$$
Prove that at least one of the numbers $a + c$ or $b + c$ is a composite number, that is, it has some divisor greater than 1 and less than itself.
$$
5 m + 8 n = 120
$$
(b) Let $a$, $b$ and $c$ be positive integers with $c \gt 1$ such that
$$
\frac{1}{a} + \frac{1}{b} = \frac{1}{c}
$$
Prove that at least one of the numbers $a + c$ or $b + c$ is a composite number, that is, it has some divisor greater than 1 and less than itself.