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Numbers in the Vertices of a Cube

Source: OMM 2008 5

July 19, 2014
geometry3D geometrygreatest common divisornumber theory unsolvednumber theory

Problem Statement

We place 88 distinct integers in the vertices of a cube and then write the greatest common divisor of each pair of adjacent vertices on the edge connecting them. Let EE be the sum of the numbers on the edges and VV the sum of the numbers on the vertices.
a) Prove that 23E≤V\frac23E\le V. b) Can E=VE=V?
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