Question 98
For any positive integer $n$ the sum $1+\frac{1}{2}+\cdots+\frac{1}{n}$ is written in the form $\frac{p_{n}}{q_{n}}$, where $p_{n}$ and $q_{n}$ are coprime numbers.
a) Prove that $3$ does not divide $p_{67}$.
b) Find all $n$, for which $3$ divides $p_{n}$.
a) Prove that $3$ does not divide $p_{67}$.
b) Find all $n$, for which $3$ divides $p_{n}$.