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Hard number theory on cubes

Source: Iranian RMM TST 2021 Day3 P3

April 16, 2021
number theorysum of cubes

Problem Statement

Let nn be an integer greater than 11 such that nn could be represented as a sum of the cubes of two rational numbers, prove that nn is also the sum of the cubes of two non-negative rational numbers.
Proposed by Navid Safaei
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