Abstract We consider the distribution of perfect squares in a Beatty sequence, which is of the form ⌊αn + β⌋. We also analyze it on average over positive square-free integers. The proof relies on a new bound of character sums with Beatty sequences, which answers an open question posted by Igor Shparlinski. MSC Numbers: 11B83; 11L07; 11L40.
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Guo et al. (2024) studied this question.
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