May 21, 2024Open Access

Small Prime kth Power Residues and Nonresidues in Arithmetic Progressions

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Abstract

Let p be a large odd prime, let x= (p) ^1+ and let q p be an integer, where >0 is a small number. This note proves the existence of small prime quadratic residues and prime quadratic nonresidues in the arithmetic progression a+qm x, with relatively prime 1 a<q, unconditionally. The same results are generalized to small prime kth power residues and nonresidues, where k p-1 and k p.

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Cite This Study

N. A. Carella (Tue,) studied this question.

synapsesocial.com/papers/68e6935fb6db643587619f89 https://doi.org/https://doi.org/10.48550/arxiv.2405.13159

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