IMO 2019 Shortlist N3
We say that a set S of integers is rootiful if, for any positive integer n and any a0,a1,...,an P S, all integer roots o...
Category: Number Theory
Problem
We say that a set S of integers is rootiful if, for any positive integer n and any
a0,a1,...,an P S, all integer roots of the polynomial a0 a1x ¨¨¨ ` anxn
are also in S. Find
all rootiful sets of integers that contain all numbers of the form 2a
´ 2b
for positive integers
a and b.
(Czech Republic)