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Found problems: 1

2021 India National Olympiad, 2
Tags: algebra , Cubics , integer roots , Vieta , INMO , v_2
Find all pairs of integers $(a,b)$ so that each of the two cubic polynomials $$x^3+ax+b \, \, \text{and} \, \, x^3+bx+a$$ has all the roots to be integers. [i]Proposed by Prithwijit De and Sutanay Bhattacharya[/i]