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Dual cubics with integer roots

Source: INMO 2021 Problem 2

March 7, 2021
algebraCubicsinteger rootsVietaINMO

Problem Statement

Find all pairs of integers (a,b)(a,b) so that each of the two cubic polynomials x3+ax+b  and  x3+bx+ax^3+ax+b \, \, \text{and} \, \, x^3+bx+a has all the roots to be integers.
Proposed by Prithwijit De and Sutanay Bhattacharya
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