Nonoverlapping pairs of explicit inversive congruential pseudorandom numbers

Recently, the explicit inversive congruential method with power of two modulus for generating uniform pseudorandom numbers was introduced. Statistical independence properties of the generated sequences have been studied by estimating the discrepancy of all overlapping pairs of successive pseudorandom numbers. In the present paper a similar analysis is performed for the subsets of nonoverlapping pairs. The method of proof relies on a detailed discussion of the properties of certain exponential sums.