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# For every positive even integer n, the function hn) is

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For every positive even integer n, the function hn) is [#permalink]  07 May 2006, 13:17
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For every positive even integer n, the function hn) is defined to be the product of all even integers from 2 to n, inclusive. If P is the smallest prime factor of h(100) + 1, the P is

A) between 2 and 10
B) between 10 and 20
C) between 20 and 30
D) between 30 and 40
E) greater than 40
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Re: PS [#permalink]  07 May 2006, 14:14
could not figure out...

also want to know the best approach how to solve it.

guess E.
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Re: PS [#permalink]  10 May 2006, 21:02
Professor wrote:
any idea????????????

Prof, You are right. It is E. Here is a link to the previous discussion..
http://www.gmatclub.com/phpbb/viewtopic.php?t=18802
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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Wow.. what a question !! And gr8 explanations too.
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Re: PS [#permalink]  11 May 2006, 07:19
1440006
Professor wrote:
any idea????????????

Since i'm not native speaker, it is sometimes hard for me to express my thoughts in english. That is why please, don't get annoyed if it is hard tp understand me.
Here is my approach:

h(100)+1=2*4*6*...*50+1 -->2*1*2*2*2*3....*2*50 + 1 -->
2^50(50!)+1
50! is number that can be divided by any prime that is less than 50(3,5,7,11...47). So 2^50*50! is 2*3*.....*5*...*13*...*47*...=
2^75*3^16*5^10*7^7*11^3*13^3*17^2*19^2*23^2*29*31*37*.....*47*.
So you may see that 2^50*50! is composed of prime numbers in different degrees.

if prime number is multiplied by another prime number, than new number's factors will all contain ONLY these primes. The same rule can be applied here.
Since 1 is less than the least prime, 2 that is, than 2^50*50! +1 wil not have any common prime factor with 2^50*50!, and since 50! has already occupied all primes that are less than 50, than prime factor of 2^50*50!+1 have to be greater than 50.

Regards,
Dilshod
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Re: PS [#permalink]  11 May 2006, 10:40
giddi77 wrote:
Professor wrote:
any idea????????????

Prof, You are right. It is E. Here is a link to the previous discussion..
http://www.gmatclub.com/phpbb/viewtopic.php?t=18802

thank you very much..
so difficult question but a simple solution...

i guess laxi has explained this one as well
Re: PS   [#permalink] 11 May 2006, 10:40
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