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
We were notified that an identical version of the paper has been published in the Journal of Integer Sequences, Vol. 16(2013), Article 13.7.8., without the author informing in advance the Editorial Board of the Notes on Number Theory and Discrete Mathematics.
The Publisher apologizes for any inconvenience caused!
On two Diophantine equations 2A6 + B6 = 2C6 ± D3
Original research paper. Pages 29—34
Susil Kumar Jena
Full paper (PDF, 138 Kb) | Abstract
An explicit estimate for the Barban and Vehov weights
Original research paper. Pages 35—43
Djamel Berkane
Full paper (PDF, 164 Kb) | Abstract

where λd 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
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

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

with f0(q) = 1, 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
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