设n为整数,使得(n^2-2n+4)是(n+3)的倍数,则满足这样条件的n值共有?个

问题描述:

设n为整数,使得(n^2-2n+4)是(n+3)的倍数,则满足这样条件的n值共有?个

n^2-2n+4
=(n+3)(n-5)+19
(n^2-2n+4)/(n+3)=n-5+19/(n+3)
n+3=±1
n+3=±19
解得:n=-4,-2,-22,16