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How many such partitions of C are there ?

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September 22, 2010
number theoryprime numberscombinatoricscomposite numberscountingIMO Shortlist

Problem Statement

Let PP be a set of 77 different prime numbers and CC a set of 2828 different composite numbers each of which is a product of two (not necessarily different) numbers from PP. The set CC is divided into 77 disjoint four-element subsets such that each of the numbers in one set has a common prime divisor with at least two other numbers in that set. How many such partitions of CC are there ?
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