Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2016 IMO Problems/Problem 4"

m (Corrected LaTeX)
m (Fixed italics)
Line 1: Line 1:
−
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 20:12, 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?

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2016_IMO_Problems/Problem_4&oldid=113502"