2

Part of 2009 IMAR Test

Problems(1)

7 vertices of a cube with value 0, eighth with value 1, increasing numbers

Source: IMAR 2009 p2

Of the vertices of a cube,

7

of them have assigned the value

0

, and the eighth the value

1

. A move is selecting an edge and increasing the numbers at its ends by an integer value

k > 0

. Prove that after any finite number of moves, the g.c.d. of the

8

numbers at vertices is equal to

1

geometrycombinatoricscombinatorial geometrygreatest common divisornumber theory