Re: math question...need help
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inutively i can see that all the prime numbers will be closed, right? since the first dude opens all the lockers...the only people to close the "prime" lockers will be the primes themselves. im too lazy to care about the rest of the lockers though, non-primes disinterest me.
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This is not correct.
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His reasoning sounds good to me, so I'm curious why you think he's wrong?
Scott
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The primes will be closed that is correct; the non-primes are not "uninteresting" is the statement I had issue with. The correct answer is that door n will be open iff n is a perfect square.
The reason the primes are closed is because they have two divisors. In general, any integer with an even number of divisors will be closed. For any integer that is not a perfect square, if a is a divisor of n then there is an integer b so that a * b = n and a will not be equal to b. Thus the divisors of n can be paired off giving that n has an even number of divisors. Perfect squares n = k^2 have the extra divisor k that can't be paired off with enough divisor. So they have an odd number of divisors. Thus, only the perfect squares will be open.
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