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2b

Part of 2003 Abels Math Contest (Norwegian MO)

Problems(1)

\sum a_i^3 \ge t(\sum a_i )^2 when a_i \in N-{0}

Source: Norwegian Mathematical Olympiad 2003 - Abel Competition p2b

2/21/2020
Let a1,a2,...,ana_1,a_2,...,a_n be nn different positive integers where n≥1n\ge 1. Show that ∑i=1nai3≥(∑i=1nai)2\sum_{i=1}^n a_i^3 \ge \left(\sum_{i=1}^n a_i\right)^2
Suminequalitiesnumber theory