若x^y-2xy+y+x^2-2x=1983,求满足条件的整数对(x,y)
问题描述：
若x^y-2xy+y+x^2-2x=1983,求满足条件的整数对(x,y)
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答
x^y-2xy+y+x^2-2x=1983x^2(y+1)-2x(y+1)+(y+1)=1984(x-1)^2(y+1)=19841984=4*496=16*124=64*31所以,y+1=496,y=495时,(x-1)^2=4,x-1=±2,x=3,或,x=-1y+1=124,y=123时,(x-1)^2=16,x-1=±4,x=5,或,x=-3y+1=31,y=30时,(x...