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We construct a set of strong recurrence which is not a van der Corput set.This shows that the class of enhanced van der Corput sets is a proper subclassof sets of strong recurrence. In addition, we derive that the class of sets ofstrong recurrence is not a subclass of van der Corput sets. This answers somequestions asked by Bergelson and Lesigne.

Distinguishing sets of strong recurrence from van der Corput Sets