Let M be the set of those natural number that can be written using only 0's and 1's ( in the decimal system). Prove that,for every natural number k, there exists a number m belongs to M such that. (1) m has exactly k 1's, and (2) m is divisible by k . (For example , if k=3, then the number 101010 belongs to M is divisble by 3.
Natural numbers
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elementary-number-theory
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1Hint: Consider specifically numbers of the form $111\ldots 1000\ldots 0$. – 2017-02-21
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0This question has been asked several times, will try and dig out a recent occurrence. – 2017-02-21