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Perfect cube when n is not divisible by 3 - JBMO Shortlist

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October 30, 2010
geometry3D geometrynumber theoryDiophantine equationnumber theory proposed

Problem Statement

Find the positive integers nn that are not divisible by 33 if the number 2n2−10+21332^{n^2-10}+2133 is a perfect cube.
[hide="Note"] [color=#BF0000]The wording of this problem is perhaps not the best English. As far as I am aware, just solve the diophantine equation x3=2n2−10+2133x^3=2^{n^2-10}+2133 where x,n∈Nx,n \in \mathbb{N} and 3∤n3\nmid n.
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