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Inequality or Not?

Source: 1989 National High School Mathematics League, Exam One, Problem 15

February 25, 2020
inequalities

Problem Statement

For any positive integer nn, an>0a_n>0, and ∑j=1naj3=(∑j=1naj)2\sum_{j=1}^{n}a_j^3=\left(\sum_{j=1}^{n}a_j\right)^2. Prove that an=na_n=n
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