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Integer...need help

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Integer...need help

by billyr » Sat Feb 14, 2009 5:17 am
For every positive even integer n, the function h(n) 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, then 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--------> answer



Thank you..
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by DanaJ » Sat Feb 14, 2009 5:26 am
What you should consider is that since h(100) = 2*4*6*...*100 = 2*(2*2)*(2*3)*(2*4)*...*(2*50). This means that h(100) is a multiple of everything from 2 to 50, so h(100)+1 will not be a multiple of everything from 2 to 50. This means that the smallest prime factor of h(100) + 1 is greater than 50, which in turn makes it greater than 40.
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