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India National Olympiad
2021 India National Olympiad
2
2
Part of
2021 India National Olympiad
Problems
(1)
Dual cubics with integer roots
Source: INMO 2021 Problem 2
3/7/2021
Find all pairs of integers
(
a
,
b
)
(a,b)
(
a
,
b
)
so that each of the two cubic polynomials
x
3
+
a
x
+
b
and
x
3
+
b
x
+
a
x^3+ax+b \, \, \text{and} \, \, x^3+bx+a
x
3
+
a
x
+
b
and
x
3
+
b
x
+
a
has all the roots to be integers.Proposed by Prithwijit De and Sutanay Bhattacharya
algebra
Cubics
integer roots
Vieta
INMO