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Let f(n) denote the sum of (all) digits of natural number n. Prove that for each natural n we can choose convenient value of natural parameter p such that the equation f(npx)=f(x) has solution in natural numbers x that doesn't contain any "9" in its notation.

Does anybody have any idea? I don't... but I hope that you do... Actually I can solve a lot of special cases on a lot of pages... but I can't solve it generally. Is there any trick or only hard work? Thank you.

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# Sum of digits equation

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