Given that K is an integer, the solution of the equation (k-99) x = 111-100x is also the value of K

(k-99)x+100x=111
(k+1)x=111
X = 111 / (K + 1) is an integer
So K + 1 is a divisor of 111
k+1=1,-1,3,-3,37,-37,111,-111
k=0,k=-2,k=2,k=-4,k=36,k=-38,k=110,k=-112

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