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Problem of the Week 897

A GCD Problem

If A is a finite set of positive integers and a is in A, let f(a) denote { a / gcd(a, b) : b in A}.

There is a set of n positive integers A with the property that the number of distinct integers in Union[f(a) : a in A] is less than n. Find such a set.

Source: April 1999 Monthly article by Granville and Roesler.
© Copyright 1999 Stan Wagon. Reproduced with permission.

7 September 1999