Volume 20 ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4 ▷ Number 5
A set of Lucas sequences
Original research paper. Pages 1–5
Krassimir Atanassov
Full paper (PDF, 146 Kb) | Abstract
Fibonacci primes
Original research paper. Pages 6–9
J. V. Leyendekkers and A. G. Shannon
Full paper (PDF, 85 Kb) | Abstract
Fibonacci primes of special forms
Original research paper. Pages 10–19
Diana Savin
Full paper (PDF, 202 Kb) | Abstract
Pages 20–28
Zhi Ren
Retraction Notice
On two Diophantine equations
Original research paper. Pages 29–34
Susil Kumar Jena
Full paper (PDF, 138 Kb) | Abstract
![Rendered by QuickLaTeX.com 2A^6 + B^6 = 2C^6 \pm D^3](https://nntdm.net/wp-content/ql-cache/quicklatex.com-81eb90b077b9880e6f47322c2f8d9081_l3.png)
![Rendered by QuickLaTeX.com (A, B, C, D)](https://nntdm.net/wp-content/ql-cache/quicklatex.com-93822c64e8ebc830026e9b9f0b89c47a_l3.png)
An explicit estimate for the Barban and Vehov weights
Original research paper. Pages 35–43
Djamel Berkane
Full paper (PDF, 164 Kb) | Abstract
where is a real valued arithmetic function called the Barban and Vehov weight and we give an explicit version of a Theorem of Barban and Vehov which has applications to zero-density theorems.
Mean values of the error term with shifted arguments in the circle problem
Original research paper. Pages 44–51
Jun Furuya and Yoshio Tanigawa
Full paper (PDF, 196 Kb) | Abstract
On certain inequalities for σ, φ, ψ and related functions
Original research paper. Pages 52–60
József Sándor
Full paper (PDF, 162 Kb) | Abstract
On rational fractions not expressible as a sum of three unit fractions
Original research paper. Pages 61–64
Simon Brown
Full paper (PDF, 80 Kb) | Abstract
![Rendered by QuickLaTeX.com (a/b < 1)](https://nntdm.net/wp-content/ql-cache/quicklatex.com-b93557ff9a74affed4e8c6654a9cce35_l3.png)
![Rendered by QuickLaTeX.com \lfloor b / a \rfloor](https://nntdm.net/wp-content/ql-cache/quicklatex.com-ea1bc3ea9673550b8571bd01aade24c5_l3.png)
![Rendered by QuickLaTeX.com < 0](https://nntdm.net/wp-content/ql-cache/quicklatex.com-83733dab9fd5def895e3fbcb75d87546_l3.png)
A note on a broken Dirichlet convolution
Original research paper. Pages 65–73
Emil Daniel Schwab and Barnabás Bede
Full paper (PDF, 185 Kb) | Abstract
![\sum\limits_{\stackrel{a\ (mod\ n)}{(a,n)_{\otimes}=1}}{(a-1,n)}=\phi_{\otimes}(n)\left\tau(n)-\frac{1}{2}\tau_{2}(n)\right \sum\limits_{\stackrel{a\ (mod\ n)}{(a,n)_{\otimes}=1}}{(a-1,n)}=\phi_{\otimes}(n)\left\tau(n)-\frac{1}{2}\tau_{2}(n)\right](http://nntdm.net/wp-content/uploads/formulas/20-2-65.png)
where (a, n)⊗ denotes the greatest common odd divisor of a and n, φ⊗(n) is the number of integers a (mod n) such that (a, n)⊗ = 1, τ(n) is the number of divisors of n, and τ2(n) is the number of even divisors of n.
On a recurrence related to 321–avoiding permutations
Original research paper. Pages 74–78
Toufik Mansour and Mark Shattuck
Full paper (PDF, 166 Kb) | Abstract
![Rendered by QuickLaTeX.com f_n(q)](https://nntdm.net/wp-content/ql-cache/quicklatex.com-c8ff4315f51407a5779da725de3878f4_l3.png)
with , which was later proven in the affirmative, see [1]. In this note, we provide a new proof of this conjecture, based on the scanning-elements algorithm described in [3], and present an identity obtained by equating two explicit formulas for the generating function
.
Nesterenko-like rational function, useful to prove the Apéry’s theorem
Original research paper. Pages 79–91
Anier Soria Lorente
Full paper (PDF, 209 Kb) | Abstract
Some arithmetic properties of an analogue of Möbius function
Original research paper. Pages 92–96
Ramesh Kumar Muthumalai
Full paper (PDF, 141 Kb) | Abstract
Volume 20 ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4 ▷ Number 5