Find all values of $a$ for which the equation $x^3 - x + a = 0$ has three different integer solutions.
Problem
Source: 2000 Estonia National Olympiad Final Round grade 11 p3
Tags: polynomial, roots, Integer, algebra
Source: 2000 Estonia National Olympiad Final Round grade 11 p3
Tags: polynomial, roots, Integer, algebra
Find all values of $a$ for which the equation $x^3 - x + a = 0$ has three different integer solutions.