请教一道PP题，急。

飞行2010

122      If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1)  2 is not a factor of n.  (2)  3 is not a factor of n.

请问大家，我选的是E，因为当n=0, or 1时，(n-1)(n+1)并不能被24整除，n=5,7...时候就可以所以不确定，可答案是C.谢谢。

escapeex

122      If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1)  2 is not a factor of n.  (2)  3 is not a factor of n.

- by 会员 飞行2010 (2010/2/5 13:28:42)

(1)  2 is not a factor of n.  

可以认为n=2x+1, 因此(n-1)(n+1)= (2x+1-1)(2x+1+1)=4*x*(x+1). x and (x+1)必有一个是偶数,因此,满足此条件时,8 is a factor of (n-1)(n+1).

(2)  3 is not a factor of n.

可以认为n=3y+1 or 3y+2, 此时,(n-1)和(n+1)中必有是3的倍数.因此,满足此条件时,3 is a factor of (n-1)(n+1).

同时满足条件(1)和(2)时, both 8 and 3 are factors of (n-1)(n+1), which means 24=3*8 is a factor of (n-1)(n+1). 此时,r=0.

选C.

philjiao

escapeex 发表于 2010-2-6 10:39
122      If n is a positive integer and r is the remainder when (n - 1)(n + 1) is  ...

感谢解答！