prep一道数学题

renxian

1.stock   numbers

  V         68

  W        112

   X          56

  y           94

  Z           45

it shows the number of shares of each of the 5 stocks owned byMr li, if Mr li wasa to sell 20 shares of stock X and buy 24 shares of stock Y, what would be the increase in the range if the numbers of the 5 tocks owned by Mr li.

2, 任意偶数n, f(n)=n个连续偶数的乘积（n>=2）,p 是h(100)+1的最小质因子，求P的范围。答案>=40

mickleon

1. Original range is 112-45=67. After transactions, X=36 and Y=118, so the new range is 118-36=82

The increasement is 82-67=15, right?

    

2. Your description of "f(n)=n个连续偶数的乘积（n>=2）" is confusing.

This should be the one you refered:

 

    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?

    

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

h(100)+1=2^50*50!+1

    


<-Personal Understanding->

Because h(100) contains all factor from 1 to 50, this means using any
value below 50 to divide h(100)+1 will result a reminder of 1. Thus the
p should be bigger than 50.