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

(In reply to Can you solve this for other n unequal 6? by JLo)

Just found a counter example to the first claim with n=8: 200, 201, 202, 203, 204, 205, 206, 207 are ALL divisible by 2, 3, 5 or 7. Even though the second claim still holds for this sequence of numbers, the example demonstrates that a proof won't be as easy as for n=6.

Posted by JLo on 2006-09-01 16:24:17