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Natural numbers on the faces of a cube

Source: Baltic Way 2004 Problem 6

November 20, 2004
geometry3D geometrynumber theory proposednumber theory

Problem Statement

A positive integer is written on each of the six faces of a cube. For each vertex of the cube we compute the product of the numbers on the three adjacent faces. The sum of these products is 10011001. What is the sum of the six numbers on the faces?