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by Carlo75 » Thu May 22, 2008 7:46 am
For every even integer n, the function h(n) is defined to be the product of all the even integer 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) greter than 40

OA is E

please explanation
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Source: — Problem Solving |

by aatech » Thu May 22, 2008 8:05 am
f(2) = 2

f(4) = 2*4

f(100) = 2*4*6..... *98*100 = 2(1*2*3*...50)
means all numbers from 1 to 50 is a factor of f(100).
in turn, means NO numbers from 1 to 50 will be factor of f(100)+1.

so, the smallest prime no that will be factor of f(100)+1 will be >50

Ans E suits that. So E
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by egybs » Thu May 22, 2008 11:01 am
This is not correct:
f(100) = 2*4*6..... *98*100 = 2(1*2*3*...50)

It would be f(100) = 2*4*6..... *98*100 = 2^(100/2)(1*2*3*...50)
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by aatech » Thu May 22, 2008 11:05 am
egybs wrote:This is not correct:
f(100) = 2*4*6..... *98*100 = 2(1*2*3*...50)

It would be f(100) = 2*4*6..... *98*100 = 2^(100/2)(1*2*3*...50)
Totally Agree
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