Let $d$ be any fixed natural number. Show that there must exist an integer of the form $11\ldots1100\ldots 00$ (that is a integer whose digits consist of a sequence of $1$'s followed by $0$'s) which is divisible by $d$.
So If $x$ is the sequence integer the I know I want to show that:
$$x \equiv 0 \mod d$$
I know that the remainder are the boxes in the pigeon hole principles. But here I am stuck on how to proceed. any help?