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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15