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 < | 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? | ||
Revision as of 19:11, 26 December 2019
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 
. What is the least possible positive integer value of 
such that there exists a non-negative integer 
for which the set 
is fragrant?
