MathDB

Given several nonnegative integers (repetitions allowed), the allowed operation is to choose a positive integer

a

and replace each number

b

greater than or equal to

a

b-a

(the numbers

a

, if any, are replaced by

0

). Initially, the integers from

1

are written on the blackboard until

2013

inclusive. After a few operations the numbers on the board have a sum equal to

10

. Determine what the numbers that remained on the board could be. Find all the possibilities.

5