1,if w,x,y and z are integers such that w/x and y/z are integers, is w/x+y/z odd?
(1)wx+yz is odd
(2)wz+xy is odd
w/x+y/z=wz+xy/xz
1)可以用举例法排除,比如X=1,Z=2,W=3,Y=4 (wx+yz is odd,w/x+y/z odd)
与X=1,Z=2,W=3,Y=6 (wx+yz is odd, w/x+y/z even)
2)w/x+y/z = (wz+xy)/xz -> wz + xy = xz * A (A denotes the sum of w/x+y/z, because w/x and y/z are integers, their sum is an integer). wz+xy is odd, so xz and A must be odd each, otherwise wz+xy is even.