Question 118
Show that there are infinitely many natural numbers $a$ and $b$ so that:
$$
a \cdot \gcd(a, b) = b + \text{lcm}(a, b),
$$
where $\gcd(a, b)$ is the greatest common divisor and $\text{lcm}(a, b)$ is the lowest common multiple of $a$ and $b$.
$$
a \cdot \gcd(a, b) = b + \text{lcm}(a, b),
$$
where $\gcd(a, b)$ is the greatest common divisor and $\text{lcm}(a, b)$ is the lowest common multiple of $a$ and $b$.