501 x 4 = 2004
111110101 in binary = 501
501x3 = 1503
= 10111011111
Since the number of ones in each are coprime, there is a way to add the digits next to each other so that 2004 1's are in the binary number. (this is the same as sticking so many zeros on the end of whichever number, i.e multiplying by 2n , then adding the other number. )
The number of zeros in the number will be < 2002 , since with each number the difference between the number of 1's and 0's is greater than 2, so the difference between the amounts of each always grows, with the number of zeros being less. when you reach a number with 2004 1's in it, multiply it by 4 (i.e, adding 2 zeros on the end) this means you will have 4 x(certain amount of 501s) which is the same as a certain number of 2004s, meaning the number is a multiple of 2004 decimal.
Adding zeros to the end of this number will simple multiply it by 2n so you can add as many zeros as you like, prefarably, the amount needed to take the amount of zeros in the number up to 2004.
That isn't a great argument, but I hope it's right lol, spent a long time squirming....attempted it a while ago with absolutely no success