Thread: natural number divisible by 2004

Hi all;

Prove that there's a natural number divisible by 2004 consisting only of zeros and sevens.

Help appreciated. Thank you.

Originally Posted by disclaimer

Hi all;

Prove that there's a natural number divisible by 2004 consisting only of zeros and sevens.

Let , , , .... .

By pigeonhole principle there are two numbers with same remainder. Thus there are with divisible by . And this number only consists of only sevens and zeros.