How to calculate the number of divisors of an integer $n$?
We use the fundamental theorem of arithmetic: $n=\prod_{i=1}^{j} p_{i}^{v_{p_{i}}(n)}$. A divisor of $n$ is of the form $\Pi_{i=1}^{j} p_{i}^{\beta_{i}}$, with $\beta_{i}$ an integer between 0 and $v_{p_{i}}(n)$. In total, there are $\prod_{i=1}^{j}\left(v_{p_{i}}(n)+1\right)$ choices for all the exponents $\beta_{i}$, which corresponds to the number of divisors.

## Chinese Remainder Theorem

Do you remember the first welcome exercise proposed in the welcome booklet?