Question 94
a) Prove that $12n+13$ and $13n+14$ are coprime, for every natural $n$.
b) Find the number of the pairs $(a, b)$ of natural numbers for which there exists a natural number $n$ so that $\frac{a}{b} = \frac{12n+13}{13n+14}$ and $17a + 19b \lt 2024$.
b) Find the number of the pairs $(a, b)$ of natural numbers for which there exists a natural number $n$ so that $\frac{a}{b} = \frac{12n+13}{13n+14}$ and $17a + 19b \lt 2024$.