MathDB
Four integers are marked on a circle

Source: IMO Shortlist 1996, N1

August 9, 2008
number theoryprime numbersgameinvariantIMO Shortlist

Problem Statement

Four integers are marked on a circle. On each step we simultaneously replace each number by the difference between this number and next number on the circle, moving in a clockwise direction; that is, the numbers a,b,c,d a,b,c,d are replaced by a\minus{}b,b\minus{}c,c\minus{}d,d\minus{}a. Is it possible after 1996 such to have numbers a,b,c,d a,b,c,d such the numbers |bc\minus{}ad|, |ac \minus{} bd|, |ab \minus{} cd| are primes?
Back to ProblemsView on AoPS