1971 IMO Problems/Problem 3
Prove that the set of integers of the form contains an infinite subset in which every two members are relatively prime.
Wlog, assume . Then say are all the (pairwise distinct) primes dividing and let . Obviously is odd, for any . So divides , by Fermat's little theorem, and . Now, by induction, it follows , for any distinct .
The above solution was posted and copyrighted by s.tringali. The original thread for this problem can be found here: 
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