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Found problems: 1

2016 District Olympiad, 3
Tags: equation , depressed cubic , cubic equation , cubic function , polynomial , algebra
[b]a)[/b] Prove that, for any integer $ k, $ the equation $ x^3-24x+k=0 $ has at most an integer solution. [b]b)[/b] Show that the equation $ x^3+24x-2016=0 $ has exactly one integer solution.