Call integer number $x$ as far from squares and cubes, if for every integer $k$ it is true : $|x-k^2|>10^6,|x-k^3|>10^6$. Prove, that there are infinitely many far from squares and cubes degrees of $2$
Source: St Petersburg Olympiad 2011, Grade 11, P4
Tags: number theory
Call integer number $x$ as far from squares and cubes, if for every integer $k$ it is true : $|x-k^2|>10^6,|x-k^3|>10^6$. Prove, that there are infinitely many far from squares and cubes degrees of $2$