100 numbers around a circle
Source: All-Russian MO 2000
December 30, 2012
number theorygreatest common divisormodular arithmeticrelatively primeRussia
Problem Statement
One hundred natural numbers whose greatest common divisor is are arranged around a circle. An allowed operation is to add to a number the greatest common divisor of its two neighhbors. Prove that we can make all the numbers pairwise copirme in a finite number of moves.