求助一道数学题

sunnylee

n is an even,H(n) represents the product of all even numbers from 2 to n.

what is the least possible prime factor of H(100)+1

A: 0-9

B 10-20

C 20-30

D greater that 40

sunnylee

thanks !!!

tongxiao88

直接知道P=h(100)+1

         =(2*4*6...*100)+1

         = 50! *2^50 +1

因为h(100)肯定可以被50以下所有的质数整除，所以h(100)+1的话不能被50以下所有的质数整除。

cherrywds

h(100)=2*4*6*...*100=(2*1)*(2*2)*(2*3)*(2*4)...*(2*50)=2^50*(1*2*3*...*50)=2^50*50!

令P*X=h(100)+1=2^50*50!+1

X=2^50*50!/p+1/p

由于X是整数,所以P>50

tongxiao88

h(100)=2*4*6*...*100=(2*1)*(2*2)*(2*3)*(2*4)...*(2*50)=2^50*(1*2*3*...*50)=2^50*50!

目前只想到这里，也想请教~