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S (n^2)/S (n) = R, sum of digits

Source: 2015 Latvia BW TST P14

December 16, 2022
number theorysum of digits

Problem Statement

Let S(a)S(a) denote the sum of the digits of the number aa. Given a natural RR can one find a natural nn such that S(n2)S(n)=R\frac{S (n^2)}{S (n)}= R?
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