MathDB
2019 Saint Peteresburg Grade 11 P2

Source:

April 14, 2019
combinatoricsnumber theorygreatest common divisor

Problem Statement

On the blackboard there are written 100100 different positive integers . To each of these numbers is added the gcd\gcd of the 9999 other numbers . In the new 100100 numbers , is it possible for 33 of them to be equal.
(С. Берлов)