Consider six consecutive positive integers. Show that there is a prime number that divides exactly one of them.

(In reply to proof2 by Art M)

Yours is a streamlined version of Tristan's proof.  The crux is that when the ends are divisble by 5, of the 4 numbers in the middle, at least one is not divisible by 2,3 or 5. Two, however can be divisible by 3, contrary to what you have said.

Posted by Richard on 2006-08-30 18:53:18