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

(In reply to re(2): n = 8... and more questions by Steve Herman)

Steve,
you are absolutely right, I was talking nonsense! Not one of my finest moments this is, I have to correct myself for the second time now. Here comes what I meant to say (I hope!!!):

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Consider n consecutive numbers. Then it is impossible that each prime number p<=n divides at least two of the n numbers and that each of the n numbers is divisible by a p<=n.
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Doesn't sound so crisp anymore... Still, when I verified n=2..14 I have acually verified the above and I still see the following questions:

- Can you prove or disprove the above, stronger statment?
- In case of disproval, what is a counter example with minimal n?
- For this minimal n, can you still prove the original puzzle?

Does that make sense?

Posted by JLo on 2006-09-07 11:18:58