MathDB
Divisors of 30030

Source: Baltic Way 2005/10

November 7, 2005
graph theorycombinatorics proposedcombinatorics

Problem Statement

Let m=30030m = 30030 and let MM be the set of its positive divisors which have exactly 22 prime factors. Determine the smallest positive integer nn with the following property: for any choice of nn numbers from MM, there exist 3 numbers aa, bb, cc among them satisfying abc=mabc=m.
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