For every positive even integer n, the function h(n) is defined to be the productive of all the even integers from 2 to n,inclusive.If p is the smallest prime factor of h(100)+1, then p is
(1) between 2 and 10
(2) between 10 and 20
(3) between 20 and 30
(4) between 30 and 40
(5) greater than 40
举报
是(5)吗?
h(100)+1=2X4X6X8X......X98X100+1=1X2X3X.....X49X50X(2的50次方)+1
则h(100)+1除以任何小于50的数都会余1,也就是h(100)+1不会被任何小于50的数整除,当然也包括任何小于40的质数.
因此最小的质因子肯定是大于40的
答案就是(5).
终于明白了,多谢.
You are welcome
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