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For every positive even integer n, the function h(n) is [#permalink]
17 Apr 2006, 00:48

1

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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

Here's what I think-
h(100) = 2*4*6*8*...100
so you can factor out 2^50 and get 2^50(1*2*3*...50) which is 2^50*50!
so h(100)+1 = 2^50*50!+1, so you know that every factor of that number up to 50 will have a remainder of 1, thus, any factor will be greater than 50.

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