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Sum of digit of 9^n is more than 9

Source: 2013 Thailand October Camp Number Theory Exam p3

March 7, 2022
number theorysum of digits

Problem Statement

Let s(n)s(n) denote the sum of digits of a positive integer nn. Prove that s(9n)>9s(9^n) > 9 for all n≥3n\geq 3.
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