2006 Alabama ARML TST Problems/Problem 12
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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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
