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China Mathematical Olympiad 1993 problem2

Source: China Mathematical Olympiad 1993 problem2

September 22, 2013
inequalitiesinequalities unsolved

Problem Statement

Given a natural number kk and a real number a(a>0)a (a>0), find the maximal value of ak1+ak2+⋯+akra^{k_1}+a^{k_2}+\cdots +a^{k_r}, where k1+k2+⋯+kr=kk_1+k_2+\cdots +k_r=k (ki∈N,1≤r≤kk_i\in \mathbb{N} ,1\le r \le k).
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