Difference between revisions of "2016 IMO Problems/Problem 4"
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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? | 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? | ||
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| + | ==Solution== | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=2016|num-b=3|num-a=5}} | ||
Revision as of 00:36, 19 November 2023
Problem
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 
. What is the least possible positive integer value of 
such that there exists a non-negative integer 
for which the set 
is fragrant?
Solution
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See Also
| 2016 IMO (Problems) • Resources | ||
| Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
| All IMO Problems and Solutions | ||
