Abstract
Let [Formula: see text] be a positive integer and let [Formula: see text] be an odd prime. For [Formula: see text], we study the distribution of consecutive square-free numbers of the forms [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text]. In addition, we study the distribution of consecutive square-free primitive roots modulo [Formula: see text] of the forms [Formula: see text],[Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], respectively.
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