If S in the infinite sequence S1=9, S2=99, S3=999,…, Sk=10k-1,…, is every term in S divisible by the prime number P?

1 P is greater than 2

2 at least one term in S is divisible by P.           

The weights of four packages are 1, 3, 5 and 7 pounds, respectively. Which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

9, 10, 12, 13, 14            

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), n is not divisible by 2; (2), n is not divisible by 3  

1，选E，e.x.可能是3，也可能是11.

2，14不可能，你怎么也加不出14来。

3，选E，e.x.:n=5时，r=12；n=7时，r=0.

3.

(1) n = 2k+1, (n-1)(n+1) = 2k(2k+2)= 4k(k+1) is divisible by 8

(2) n= 3k+1 or 3k+2, (n-1)(n+1) = 3k*(3k+2) or (3k+1)(3k+3), both are divisible by 3

If we combine (1) and (2), then n is surely divisible by 24. Thus the remainder r is always 0.

The answer should be (C)