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2016 IMO Problems/Problem 4: Difference between revisions

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A set of postive integers is called [i]fragrant[/i] 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 <math>P(n)=n^2+n+1</math>.  What is the least possible positive integer value of <math>b</math> such that there exists a non-negative integer <math>a</math> for which the set <math>\{P(a+1),P(a+2),\ldots,P(a+b)\}</math> is fragrant?
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 <math>P(n)=n^2+n+1</math>.  What is the least possible positive integer value of <math>b</math> such that there exists a non-negative integer <math>a</math> for which the set <math>\{P(a+1),P(a+2),\ldots,P(a+b)\}</math> is fragrant?

Revision as of 19:12, 26 December 2019

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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