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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.


Solution Summary

This is a discrete math proof of divisibility.