When x 13 + 1 is divided by x - 1, then what is the remainder?

According to the Remainder Theorem, when a polynomial expression $f(x)$ is divided by a linear term $(x-c)$, the resulting remainder is equal to $f(c)$.Here, our polynomial function is:
$$f(x)=x^{13}+1$$
The divisor is $x-1$, so we set $c=1$.Finding the remainder by evaluating $f(1)$:
$$\text{Remainder}=f(1)=(1{)}^{13}+1$$
$$\text{Remainder}=1+1=2$$