MathDB

Written on a blackboard are

n

nonnegative integers whose greatest common divisor is

1

. A move consists of erasing two numbers

x

and

y

, where

x\ge y

, on the blackboard and replacing them with the numbers

x-y

and

2y

. Determine for which original

n

-tuples of numbers on the blackboard is it possible to reach a point, after some number of moves, where

n-1

of the numbers of the blackboard are zeroes.

Problem Statement