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diophantine with integer parameter: x^3\pm 24x+k=0

Source: Romanian District Olympiad 2016, Grade VIII, Problem 3

October 4, 2018
algebrapolynomialequationdepressed cubiccubic equationcubic function

Problem Statement

a) Prove that, for any integer k, k, the equation x3−24x+k=0 x^3-24x+k=0 has at most an integer solution.
b) Show that the equation x3+24x−2016=0 x^3+24x-2016=0 has exactly one integer solution.
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