Difference between revisions of "2006 Alabama ARML TST Problems/Problem 12"
(New page: ==Problem== Yoda begins writing the positive integers starting from 1 and continuing consecutively as he writes. When he stops, he realizes that there is no set of 5 composite integers amo...) |
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Revision as of 11:32, 17 April 2008
Problem
Yoda begins writing the positive integers starting from 1 and continuing consecutively as he writes. When he stops, he realizes that there is no set of 5 composite integers among the ones he wrote such that each pair of those 5 is relatively prime. What’s the largest possible number Yoda could have stopped on?
Solution
The least group of 5 positive consecutive integers with the property that each pair of those is relatively prime is the set 
. Therefore, the largest number he could have stopped on is 
.
