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We give a method of constructing cocyclic subshifts from Diophantine equations. As an application, we produce examples of such subshifts that are not sofic and prove that the problem of equality of two cocyclic subshifts is algorithmically undecidable. (The last result already follows from 1970 work by Paterson on mortality of matrices.)doi:10.1080/14689367.2013.844225 fatcat:d2pqb336fncgxpe2bnkdhwnvea