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p_1^2 + p_2^2 + · · + p_n^2 > n^3

Source: Switzerland - 2013 Swiss MO Final Round p2

December 30, 2022
inequalitiesnumber theoryprimes

Problem Statement

Let nn be a natural number and p1,...,pnp_1, ..., p_n distinct prime numbers. Show that p12+p22+...+pn2>n3p_1^2 + p_2^2 + ... + p_n^2 > n^3
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