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标题: 请教两题 [打印本页]

作者: LHL888 时间: 2005-6-16 06:27 标题: 请教两题

1. The pages of a report are numbered consecutively from 1 to 10. If the sum of the page numbers up to and including page number x of the report is equal to one more than the sum of the page numbers following page number x, then x =

A) 4 B) 5 C) 6 D) 7 E) 8

Answer: D

2) If n and p are different positive prime numbers, which of the integers n^4, P^3, and np has (have) exactly 4 positive divisors?

A) n^4 only
B) p^3 only
C) np only
D) n^4 and np
E) p^3 and np

Answer: E

Can anyone explain above two questions? Thanks!

作者: liuliyun 时间: 2005-6-16 12:44

1、（1+X）*X/2 = （X + 1 + 10）*（10 - X）/2 + 1 所以X = 7

2、任何一个integers，最简因式分解后（分解成因子全部为质数），全部的positive divisors为每一个质因子（指数 + 1）的乘积！比如此道题目： n^4 为 4+1=5 P^3 为 3+1=4 np 为（1+1）*（1+1）=4

所以选E！

作者: LHL888 时间: 2005-6-18 06:23

明白了，谢谢解答！！

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