Counting the solutions of \(\lambda_1 x_1^{k_1} + \dots + \lambda_t x_t^{k_t} \equiv c \bmod n\)

DOI10.1016/J.JNT.2017.10.017zbMath1430.11047arXiv1705.07584OpenAlexW2770778184MaRDI QIDQ1747211

Yi Ouyang, Song-Song Li

Publication date: 4 May 2018

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

Full work available at URL: https://arxiv.org/abs/1705.07584

zbMATH Keywords

squares of unitscongruence equationdecomposition and lifting of residue classespowers of units

Mathematics Subject Classification ID

Gauss and Kloosterman sums; generalizations (11L05) Congruences in many variables (11D79) Arithmetic functions; related numbers; inversion formulas (11A25) Additive bases, including sumsets (11B13) Trigonometric and exponential sums (general theory) (11L03)

Related Items (3)

On the number of unit solutions of cubic congruence modulo \(n\) ⋮ On binary quadratic forms modulo \(n\) ⋮ Fast computation of the number of solutions to \(x_1^2 + \cdots + x_k^2 \equiv \lambda \pmod{n}\)

Cites Work

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• On the addition of squares of units modulo \(n\)
• Quadratic equations over finite fields and class numbers of real quadratic fields
• On the addition of squares of units and nonunits modulo \(n\)
• On the addition of two weighted squares of units mod n
• Counting invertible sums of squares modulo $n$ and a new generalization of Euler's totient function
• On the sumset of atoms in cyclic groups
• Counting solutions of quadratic congruences in several variables revisited

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