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Smallest n with 4S(n)=3S(2n)

Source: Czech-Polish-Slovak Junior Match 2024, I-5

May 29, 2024
number theorynumber theory proposedsum of digits

Problem Statement

For a positive integer nn, let S(n)S(n) be the sum of its decimal digits. Determine the smallest positive integer nn for which 4⋅S(n)=3⋅S(2n)4 \cdot S(n)=3 \cdot S(2n).
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