MathDB
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, 77 of them have assigned the value 00, and the eighth the value 11. A move is selecting an edge and increasing the numbers at its ends by an integer value k>0k > 0. Prove that after any finite number of moves, the g.c.d. of the 88 numbers at vertices is equal to 11.
Russian M.O.