7 vertices of a cube with value 0, eighth with value 1, increasing numbers
Source: IMAR 2009 p2
September 27, 2018
geometrycombinatoricscombinatorial geometrygreatest common divisornumber theory
Problem Statement
Of the vertices of a cube, of them have assigned the value , and the eighth the value . A move is selecting an edge and increasing the numbers at its ends by an integer value . Prove that after any finite number of moves, the g.c.d. of the numbers at vertices is equal to .Russian M.O.