[讨论]一道pp数学题。。。想了好久了。。。

小白宝宝

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 smallelst 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

wendy0000001

啊，这道  同问~

蓝色回忆

e吧

h(100)和h(100)+1互质,而p是后者的factor，说明p和h(100)互质

h(100)=2^50*1*2*3*...*50，说明p>50

[此贴子已经被作者于2009-4-26 22:37:04编辑过]

wendy0000001

不太明白h(100)=2^50*1*2*3*...*50怎么得来的？

还有为什么P>50？这里有什么说法么？

snow13

h(100)+1=(2*4*6*8....*98*100)+1
        =[(2*1)*(2*2)*(2*3)*(2*4).....*(2*49)*(2*50)]+1
        =2^50*(1*2*3.....*49*50)+1
        =2^50*50!+1

如果P=45，因为在2^50*50！中有因数45，所以可以整除45，但加1后就不能整除，余数为1
所以能够被2^50*50!+1整除的数，一定大于50。

wendy0000001

明白了 谢谢好心MM