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IMO 2016 Problem 4

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IMO 2016 Problem 4

Post Number:#1  Unread postby Phlembac Adib Hasan » Sun Aug 07, 2016 1:03 pm

A set of positive 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?
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Phlembac Adib Hasan
 
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