Question

设集合M={z|z=x2—y2,x,y属于Z}

Answer 1

z=(x+y)(x-y)

1:属于:(1+0)(1-0)=1;(2+1)(2-1)=3;(3+2)(3-2)=5;(0+0)(0-0)=0;(2+0)(2-0)=4;(3+1)(3-1)=8

2:1,3,5倒是能推出所有的奇数都属于m;0,4,8是?

3:能:设Z1=(x1)2-(y1)2,z2=(x2)2-(y2)2

Z1*z2=(x1x2)2-(x1y2)2-(x2y1)2+(y1y2)2

=(x1x2)2+2*x1x2y1y2+(y1y2)2-[(x1y2)2+2*x1y2x2y1+(x2y1)2]

=(x1x2+y1y2)2-(x1y2+x2y1)2(括号外的2是平方)