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Integrability conditions for difference equations admitting a second orderformal recursion operator are presented and the derivation of symmetries andcanonical conservation laws is discussed. In the generic case, nonlocalconservation laws are also generated. A new integrable equation satisfying thesecond order integrability conditions is presented and its integrability isestablished by the construction of symmetries, conservation laws and a 3x3 Laxrepresentation. Finally, the relation of the symmetries of this equation to ageneralized Bogoyavlensky lattice and a new integrable lattice are derived.

Second order integrability conditions for difference equations. An integrable equation