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We establish new results on sets of recurrence and van der Corput sets in Z^kwhich refine and unify some of the previous results obtained by Sarkozy,Furstenberg, Kamae and Mendes France, and Bergelson and Lesigne. The proofsutilize a general equidistribution result involving prime powers which is ofindependent interest.

Uniform Distribution of Prime Powers and sets of Recurrence and van der Corput sets in Z^k