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Verbal proof is preferred as I'm not to familiar with mathematical notation.

knowbuddy
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  • Have you tried proving that if the digit sum is composite, then the number whose digits are only $1$'s is composite? – N. F. Taussig Jun 13 '15 at 11:26
  • 11 is an example. Did you find any other examples? Where did you find this claim, any reference? And, you do assume base 10, or do you consider other bases? Without some more input this question will probably be put on hold. – kjetil b halvorsen Jun 13 '15 at 17:54

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Yes, because otherwise the number can be split into equal blocks.

eg $111111=111 \text { } 111$ is clearly divisible by $111$ - and that happens because the number of $1$s in the original number is divisible by $3$.

Mark Bennet
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