Abstract
Let [Formula: see text] be an odd prime. We study the distribution of consecutive quadratic residues modulo [Formula: see text] in non-homogeneous Beatty sequences [Formula: see text], where [Formula: see text] and [Formula: see text] is irrational. Furthermore, we study the pseudorandom properties of sequences formed by the Legendre symbol and Beatty sequences. In addition, we give upper bounds for certain character sums over [Formula: see text].
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