问一道质因数的题

lunasea

For every positive integer n, the function h(n) is defined to be the product of all of the 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
h(100) = 2*4*6*....*100
i.e., h(100) = (1*2*3*....*50)*2^50
i.e., h(100) +1 = [50!*2^50] + 1

Max prime factor in 50! is 47
i.e., 50!*2^50 is divisble by 47
i.e., 50!*2^50 + 1 is NOT divisble by 47
i.e., 50!*2^50 + 1 is NOT divisble by ANY prime factor less than or equal to 47

Hence p is greater than 47 ... answer E is the best.

我想问的是47是50！的最大质因数 那为什么是H(100+1)的最小质因数呢

脑子别住了

lw666777

貌似最小质因数不都是1嘛..