A positive integer has $1001$ digits all of which are $1$’s. When this number is divided by $1001$ find the remainder

Question

A positive integer has $1001$ digits all of which are $1$'s. When this number is divided by $1001$ find the remainder.

I tried to think on it but couldn't get through. Please help.

Answer 1

$10^3\equiv-1\bmod1001$

$10^{999}\equiv-1\bmod1001$

$10^{1001}\equiv-100\equiv901\bmod1001$

$10^{1001}-1\equiv900\bmod1001$

$\dfrac{10^{1001}-1}9\equiv100\bmod1001$