Congruences involving alternating harmonic sums modulo pαqβ
-
Zhongyan Shen
and
Tianxin Cai
Abstract
In 2014, Wang and Cai established the following harmonic congruence for any odd prime p and positive integer r,
where
In this note, we obtain the congruences for distinct odd primes p, q and positive integers α, β,
and
This work is supported by the Natural Science Foundation of Zhejiang Province, Project (No. LY18A010016) and the National Natural Science Foundation of China, Project (No. 11571303)
Communicated by Federico Pellarin
Acknowledgement
The authors would like to thank the referee for his/her valuable comments and suggestions, and also the authors thank the China Scholarship Council for supporting our research.
References
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© 2018 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Prof. RNDr. Beloslav Riečan, DrSc., Dr.h.c. *NOV. 10, 1936 – †AUG. 13, 2018
- On the n × n × n Rubik's Cube
- Congruences involving alternating harmonic sums modulo pαqβ
- On the proximity of large primes
- On the factorizations of cubic polynomials with the same discriminant modulo a prime
- Some results on abstract convexity of functions
- Remarks on b-Metric and metric-preserving functions
- Generalization of Ostrowski inequality for convex functions
- On microscopic sets and Fubini Property in all directions
- New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator
- Application of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equations
- Approximate sentinels for diffusion phenomena with pollution
- Remarks on a semilinear system in ℝn motivated by difference equations
- Oscillation tests for difference equations with several non-monotone deviating arguments
- On the regularity of one-sided fractional maximal functions
- A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space
- A note about Volterra operator
- Some reverse and numerical radius inequalities
- A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds
- Sequential decreasing strong size properties
- Approximation of Information Divergences for Statistical Learning with Applications
- Wigner's theorem for an infinite set
- A note on automorphisms of lie ideals in prime rings
Articles in the same Issue
- Prof. RNDr. Beloslav Riečan, DrSc., Dr.h.c. *NOV. 10, 1936 – †AUG. 13, 2018
- On the n × n × n Rubik's Cube
- Congruences involving alternating harmonic sums modulo pαqβ
- On the proximity of large primes
- On the factorizations of cubic polynomials with the same discriminant modulo a prime
- Some results on abstract convexity of functions
- Remarks on b-Metric and metric-preserving functions
- Generalization of Ostrowski inequality for convex functions
- On microscopic sets and Fubini Property in all directions
- New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator
- Application of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equations
- Approximate sentinels for diffusion phenomena with pollution
- Remarks on a semilinear system in ℝn motivated by difference equations
- Oscillation tests for difference equations with several non-monotone deviating arguments
- On the regularity of one-sided fractional maximal functions
- A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space
- A note about Volterra operator
- Some reverse and numerical radius inequalities
- A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds
- Sequential decreasing strong size properties
- Approximation of Information Divergences for Statistical Learning with Applications
- Wigner's theorem for an infinite set
- A note on automorphisms of lie ideals in prime rings
