2006 Alabama ARML TST Problems/Problem 12
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 .
See also
2006 Alabama ARML TST (Problems) | ||
Preceded by: Problem 11 |
Followed by: Problem 13 | |
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