Partitions into two Lehmer numbers in ℤq
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Jiankang Wang
Abstract
Let ℤq be a complete residue system modulo an odd integer q ≥ 3. The main purpose of this paper is to give an asymptotic formula for the number of representations of an element n ∈ ℤq as sum of two classical Lehmer numbers in ℤq. In addition, we make explicit the known expression for the number of the classical Lehmer numbers.
Funding statement: This work is supported by National Natural Science Foundation of China (12471006, 12371007) and Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY007).
(Communicated by István Gaál)
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Articles in the same Issue
- Generalized Sasaki mappings in d0-Algebras
- On a theorem of Nathanson on Diophantine approximation
- Constructing infinite families of number fields with given indices from quintinomials
- Partitions into two Lehmer numbers in ℤq
- Fundamental systems of solutions of some linear differential equations of higher order
- On k-Circulant matrices involving the Lucas numbers of even index
- Explicit formulae for the Drazin inverse of the sum of two matrices
- On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
- Novel generalized tempered fractional integral inequalities for convexity property and applications
- Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
- The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
- Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
- Improvements on the Leighton oscillation theorem for second-order dynamic equations
- Topogenous orders on forms
- Comparison of topologies on fundamental groups with subgroup topology viewpoint
- An elementary proof of the generalized Itô formula
- Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
- Advancing reliability and medical data analysis through novel statistical distribution exploration
- Historical notes on the 75th volume of Mathematica Slovaca - Authors of the first issue from 1951
