Find the remainder when $r^{13} + 1$ is divided by $r - 1$.
I know that the remainder theorem says that the remainder when a polynomial $f(r)$ is divided by $r - a$ is equal to $f(a)$, the value of the polynomial at $r = a$. So in this case, I can use the remainder theorem and plug in $r = 1$ into the polynomial $r^{13} + 1$ to get the remainder. That means the remainder is $1^{13} + 1 = 2$. 