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Kazakhstan National Olympiad 2014 P3 D2 10 grade

Source: Kazakhstan National Olympiad 2014 P3 D2 10 grade

March 17, 2014
inequalitiesnumber theory proposednumber theoryKazakhstan

Problem Statement

Prove that, for all n∈Nn\in\mathbb{N}, on [n−4n,n+4n] [n-4\sqrt{n}, n+4\sqrt{n}] exists natural number k=x3+y3k=x^3+y^3 where xx, yy are nonnegative integers.
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