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This correspondence presents the remainder-quotient (RQ)-algorithm for the resolution of Boolean equations. If [mi]w = w ( xkl, xj2, ... XkN) = 1[/mi] is the Boolean equation equivalent to the system whose solution is desired, we want to determine the Boolean functions [mi]xk, = Xkp ( xhj+1,... -xkN)[/mi] with p = 1,2,... j, which verify the equivalent equation. We start with the function w given by its minterm numbers and performing usual divisions we determine the solutions in the domain of the numerical transform (NT), introduced in a previous paper. An alternative way is also presented, which is advantageous when the number of minterms in the equivalent equation is large. Examples which show the great systematization of the methods are given.