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sum of digits S(3^n) >= S(3^{n+1})- All-Russian MO 1997 Regional (R4) 11.3

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September 24, 2024
number theorysum of digits

Problem Statement

Let us denote by S(m)S(m) the sum of the digits of the natural number mm. Prove that there are infinitely many positive integers nn such that S(3n)≥S(3n+1).S(3^n) \ge S(3^{n+1}).
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