6、If x and y are integers and xy<>0, what is the remainder when x is divided by y? (1) when x is divided by 2y, the remainder is 4; (2) when x+y is divided by y, the remainder is 4;
9、If n=p/q，and both of p and q are non-zero integers, is n an integer? (1) n^2 is an integer; (2) n^3 is an integer;
谢谢。作者: LilyJune 时间: 2008-5-15 19:58
6. (1) X=2Yn+4, Y=3,5,6,7,8,9,10..., X(can be)=10,14,16,18,20,22,24, then the remainders when x is divided by y are 1,4,4,4,4,4,4....that means, if Y<4, then the remainder is 1, if Y>4, then the remainder is 4, so NO. (2) X+Y=Yn+4, X=Y(n-1)+4, Y=3,5,....X=4,9.... the remainders are 1,4,....., so NO if (1)+(2), X=4,14...y=3,5, the remainders are 1,4,.. So, E 9. (1)n^2 is an integer, if n is not an integer, then n must be an irrational number, but n=p/q must be a rational number, so n must be an integer. (2)n^3 is an integer, the same thing. so D. I don't know whether the answers are correct.作者: shelleyzhdai 时间: 2008-5-15 20:25
