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(2x^3 - 6x^2 - 3x -20)/5(x - 4) is an integer

Source: 2021 Dürer Math Competition Finals Day2 E5 https://artofproblemsolving.com/community/c2749870_

January 8, 2022
number theoryInteger

Problem Statement

How many integers 1≤x≤20211\le x \le 2021 make the value of the expression 2x3−6x2−3x−205(x−4)\frac{2x^3 - 6x^2 - 3x -20}{5(x - 4)} an integer?
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