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The notion of Laplace invariants is transferred to the lattices and discreteequations which are difference analogs of hyperbolic PDE's with two independentvariables. The sequence of Laplace invariants satisfy the discrete analog oftwodimensional Toda lattice. The terminating of this sequence by zeroes isproved to be the necessary condition for existence of the integrals of theequation under consideration. The formulae are presented for the highersymmetries of the equations possessing integrals. The general theory isillustrated by examples of difference analogs of Liouville equation.Comment: LaTeX, 15 pages, submitted to Teor. i Mat. Fi

Discrete analogues of the Liouville equation