IMO 2020 Shortlist A2
Let A denote the set of all polynomials in three variables x,y,z with integer coefficients. Let B denote the subset of A...
Category: Algebra
Problem
Let A denote the set of all polynomials in three variables x,y,z with integer
coefficients. Let B denote the subset of A formed by all polynomials which can be expressed as
px y zqPpx,y,zq pxy yz zxqQpx,y,zq xyzRpx,y,zq
with P,Q,R P A. Find the smallest non-negative integer n such that xi
yj
zk
P B for all non-
negative integers i,j,k satisfying i j k ě n.
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