Congruences for q[p/8] (mod p) under the condition 4n2p = x2 + qy2

DOI10.1142/S1793042115500700zbMath1390.11012OpenAlexW2084766291MaRDI QIDQ5253885

Zhi-Hong Sun

Publication date: 5 June 2015

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042115500700

zbMATH Keywords

binary quadratic formreciprocity lawcongruenceoctic residuequartic Jacobi symbol

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Congruences; primitive roots; residue systems (11A07) Power residues, reciprocity (11A15)

Cites Work

• Diophantine determinations of \(3^{(p-1)/8}\) and \(5^{(p-1)/4}\)
• Residuacity of primes
• Quartic, octic residues and Lucas sequences
• Some new residuacity criteria
• On the quadratic character of quadratic units
• Quartic residues and binary quadratic forms
• Supplements to the theory of quartic residues
• Congruences for q^[p/8(mod p)]
• Classical congruences for parameters in binary quadratic forms

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