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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!
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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!

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明白了,谢谢解答!!

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