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In order to analyze certain types of combinations of multiple recur- sive linear congruential generators (MRGs), we introduce a generalized spectral test. We show how to apply the test in large dimensions by a recursive pro- cedure based on the fact that such combinations are subgenerators of other MRGs with composite moduli. We illustrate this with the well-known RAN- MAR generator. We also design an algorithm generalizing the procedure to arbitrary random number generators.

Orbits and lattices for linear random number generators with composite moduli