数学题，高手来啊~

丫丫yoyo

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 for factor of h(100)+1, then p is
答案是greater than 40
求思路

fengshou

这题有被讨论过 以下是某位高人滴答案：

According to the given function,
h(100) = 2*4*6*8*...*100

By factoring a 2 from each term of our function, h(100) can be rewritten as
2^50*(1*2*3*...*50).

Thus, all integers up to 50 - including all prime numbers up to 50 - are factors of h(100).

Therefore, h(100) + 1 cannot have any prime factors 50 or below, since dividing this value by any of these prime numbers will yield a remainder of 1.

Since the smallest prime number that can be a factor of h(100) + 1 has to be greater than 50, The correct answer is E.