MathDB
ASU 409 All Soviet Union MO 1985 (a,b,c,d) -> (a-b,b-c,c-d,d-a)

Source:

August 5, 2019
gamecombinatoricsgame strategyalgebra

Problem Statement

If there are four numbers (a,b,c,d)(a,b,c,d) in four registers of the calculating machine, they turn into (ab,bc,cd,da)(a-b,b-c,c-d,d-a) numbers whenever you press the button. Prove that if not all the initial numbers are equal, machine will obtain at least one number more than 19851985 after some number of the operations.