Question 64
Find the positive integers $a$ and $b$ fulfilling
$$
\frac{a}{(a,b)} = b + \frac{48 \cdot (a,b)}{[a,b]} \quad \text{and} \quad \frac{b}{(a,b)} = a - \frac{312 \cdot (a,b)}{[a,b]}
$$
where $(a, b) = \gcd(a, b)$ and $[a, b] = \text{lcm}(a, b)$.
$$
\frac{a}{(a,b)} = b + \frac{48 \cdot (a,b)}{[a,b]} \quad \text{and} \quad \frac{b}{(a,b)} = a - \frac{312 \cdot (a,b)}{[a,b]}
$$
where $(a, b) = \gcd(a, b)$ and $[a, b] = \text{lcm}(a, b)$.