Optimal bounds for Büchi's problem in modular arithmetic

DOI10.1016/j.jnt.2014.10.008zbMath1369.11015arXiv1905.01411OpenAlexW2080569510MaRDI QIDQ2254228

Xavier Vidaux, Pablo Sáez, Maxim Vsemirnov

Publication date: 4 February 2015

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

Full work available at URL: https://arxiv.org/abs/1905.01411

zbMATH Keywords

quadratic nonresidueBüchi sequenceHensley sequencesquares in arithmetic progression

Mathematics Subject Classification ID

Finite fields and commutative rings (number-theoretic aspects) (11T99) Sequences (mod (m)) (11B50) Calculation of integer sequences (11Y55)

Related Items (1)

Büchi’s Problem in Modular Arithmetic for Arbitrary Quadratic Polynomials

Uses Software

• PARI/GP
• Xcas
• OEIS
• Python

Cites Work

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• A survey on Büchi's problem: new presentations and open problems
• Powerful values of polynomials and a conjecture of Vojta
• On lower estimates of incomplete character sums of polynomials
• Topics in multiplicative number theory
• The least quadratic non residue
• Büchi's problem in any power for finite fields
• The distribution of quadratic residues and non‐residues
• Explicit Bounds for Primality Testing and Related Problems
• Advanced Topics in Computional Number Theory
• On Some Exponential Sums

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