MathDB

On a blackboard there are

2010

natural nonzero numbers. We define a "move" by erasing

x

and

y

with

y\neq0

and replacing them with

2x+1

and

y-1

, or we can choose to replace them by

2x+1

and

\frac{y-1}{4}

y-1

is divisible by 4.
Knowing that in the beginning the numbers

2006

and

2008

have been erased, show that the original set of numbers cannot be attained again by any sequence of moves.

Problem Statement