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The main purpose of this paper is to determine the general (and also the continuous) solutions of the discrete wave equation, that is, to solve the following partial difference equation$$\underset{(x)}{\Delta^{2}_{1}}u(x, y)=\underset{(y)}{\Delta^{2}_{1}}u(x, y).$$Δ12(x)u(x,y)=Δ12(y)u(x,y).

On a discrete version of the wave equation