6. Determine the prime number $p$ such that $\frac{4}{23}<\frac{1}{p}<\frac{8}{19}$.
First method:

If we expand the fractions so that their numerators are 8, then $\frac{8}{46}<\frac{8}{8 p}<\frac{8}{19}$. 2 POINTS Further, it follows that $19<8 p<46$.

2 POINTS

This means that $8 p \in\{24,32,40\} \quad 2$ POINTS

or $p \in\{3,4,5\}$. 2 POINTS

Since $p$ is a prime number, then $p \in\{3,5\}$. 2 POINTS

TOTAL 10 POINTS