In the rectangular coordinates,abscissa and ordinate of the

In the rectangular coordinates,abscissa and ordinate of the intersection point of the lines y=x-k
and ordinate of the intersection point of the lines y=x-k and y=kx+2 are integers for integer k,then the number of the possible values(数学题昂,建议会英语的数学佼佼者来回答）

在直角坐标系中,直线y=x-k横纵坐标与直角坐标系的交点是整数,y=x-k 和 y=kx+2的交点的纵坐标是整数,就求区域中符合条件的整数K.
第一个条件好满足,只要k为整数就行,第二个就要求出交点的纵坐标y=(-k的平方-2)/(k-1),
再用基本的知识化解得,y=-k-1-3/(k-1),发现k只能填2.我想说,您从搞搞到这么自残的题啊?