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    Discrete Proof of Divisibility

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    Let d,m and n be positive integers with m>1 and m≡ 1 (mod d), let

    n= c0+mc1+m2c2+m3c3+...+mrcr

    be the base=m expansion of n, and let

    f = c0+c1+c2+c3+...+cr

    Prove that n is divisible by d if and only if f is divisible by d.

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    Solution Summary

    This is a discrete math proof of divisibility.