Prove that there is a positive multiple of 3333 which is entirely made of 0s and 1s. (For example: 110000011; note that we don’t need to find the number. We just need to prove that there exists such a number)
is multiple of 1111 since
Also N is divisible by 3 since the sum of its digits is 12, which is divisible by 3.
Since 1111 and 3 are mutually prime, from divisibility of N by 1111 and by 3 we have that N is multiple of 3333.
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