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Wavelength division multiplexing (WDM) effectively multiplies the bandwidth of an optic fiber by transmitting data over several different wavelengths on the same fiber. WDM is widely used to handle the ever-increasing demand for bandwidth in fiber optic telecommunication networks. Routing and wavelength assignment (RWA) is a critical problem to be addressed in WDM optical telecommunication networks. The goal of RWA is to maximize throughput by optimally and simultaneously assigning routes and wavelengths for a given pattern of routing or connection requests. In this paper, we present a novel technique to solve the static RWA problem using Boolean satisfiability (SAT). After formulating the RWA problem as a SAT instance, we utilize a very efficient SAT solver to find a solution. We report results for networks with and without wavelength translation capabilities in the nodes. In both cases we obtain an assignment in significantly less than one second (which is 3-4 orders of magnitude faster than existing approaches) for a set of benchmark problems. Our technique can handle arbitrary network topologies, and, due to its efficiency, can be extended to handle dynamic RWA instances, in which the network topology, link capacities and connection requests are time-varying.