cube with numbers
Source: All-Russian Olympiad 1996, Grade 10, Second Day, Problem 5
April 18, 2013
geometry3D geometrygreatest common divisornumber theory proposednumber theory
Problem Statement
At the vertices of a cube are written eight pairwise distinct natural numbers, and on each of its edges is written the greatest common divisor of the numbers at the endpoints of the edge. Can the sum of the numbers written at the vertices be the same as the sum of the numbers written at the edges?A. Shapovalov