求解一道prep数学题

fancy很简单

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

• Abetween 2 and 10
• Bbetween 10 and 20
• Cbetween 20 and 30
• Dbetween 30 and 40
• Egreater than 40
  

  答案: E

evelynizzy

h(n)=2*4*6*……*100+1=（2*1）*（2*2）*（2*3）*……*（2*50）+1=2^50*（1*2*3……*50）+1
所以h（n）被2到50任意一个数除都余1，也就是都不能被整除啦，那么它最小的质因子一定是个大于50的数，所以选E~

fancy很简单

evelynizzy 发表于 2015-8-25 18:56
h(n)=2*4*6*……*100+1=（2*1）*（2*2）*（2*3）*……*（2*50）+1=2^50*（1*2*3……*50）+1
所以h（n）被2 ...