IMO 2019 Shortlist N6
Let H “ X i ? \ : i P Zą0 ( “ t1,2,4,5,7,...u, and let n be a positive integer. Prove that there exists a constant C suc...
Category: Number Theory
Problem
Let H “
X
i
?
: i P Zą0
(
“ t1,2,4,5,7,...u, and let n be a positive integer. Prove
that there exists a constant C such that, if A Ă t1,2,...,nu satisfies |A| ě C
?
n, then there
exist a,b P A such that a´b P H. (Here Zą0 is the set of positive integers, and tzu denotes the
greatest integer less than or equal to z.)
(Brazil)