MathDB
Sum of digits

Source: Polish MO second round 2012

February 19, 2012
inductionnumber theory unsolvednumber theory

Problem Statement

Denote by S(k)S(k) the sum of the digits in the decimal representation of kk. Prove that there are infinitely many n∈Z+n\in \mathbb{Z_{+}} such that: S(2n+n)<S(2n){S(2^{n}+n})<S(2^{n}).
Back to ProblemsView on AoPS