IMO Shortlist 2016 problem N3


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3. listopada 2019.
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A set of postive integers is called fragrant if it contains at least two elements and each of its elements has a prime factor in common with at least one of the other elements. Let P(n)=n^2+n+1. What is the least possible positive integer value of b such that there exists a non-negative integer a for which the set \{P(a+1),P(a+2),\ldots,P(a+b)\}is fragrant?

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf