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ASU 294 All Soviet Union MO 1980 n+S(n)=1980, sum of digits

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July 19, 2019
sum of digitsnumber theory

Problem Statement

Let us denote with S(n)S(n) the sum of all the digits of nn.
a) Is there such an nn that n+S(n)=1980n+S(n)=1980?
b) Prove that at least one of two arbitrary successive natural numbers is representable as n+S(n)n + S(n) for some third number nn.
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