**Volume 30** ▶ Number 1 ▷ Number 2 ▷ Number 3 (Online First)

**MIN-turns and MAX-turns in k-Dyck paths: A pure generating function approach**

*Original research paper. Pages 213–222*

Helmut Prodinger

Full paper (PDF, 188 Kb) | Abstract

**Some new results on the negative polynomial Pell’s equation**

*Original research paper. Pages 223–235*

K. Anitha, I. Mumtaj Fathima, and A. R. Vijayalakshmi

Full paper (PDF, 259 Kb) | Abstract

**Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II**

*Original research paper. Pages 236–252*

A. M. S. Ramasamy

Full paper (PDF, 284 Kb) | Abstract

**On some identities for the DGC Leonardo sequence**

*Original research paper. Pages 253–270*

Çiğdem Zeynep Yılmaz and Gülsüm Yeliz Saçlı

Full paper (PDF, 261 Kb) | Abstract

**The generalized order ( k,t)-Mersenne sequences in groups**

*Original research paper. Pages 271–282*

E. Mehraban, Ö. Deveci, E. Hincal

Full paper (PDF, 302 Kb) | Abstract

**Some infinite series summations involving linear recurrence relations of order 2 and 3**

*Original research paper. Pages 283–310*

Anthony G. Shannon, Peter J.-S. Shiue, Shen C. Huang, Ali Balooch, Yu-Chung Liu

Full paper (PDF, 319 Kb) | Abstract

**The error term of the sum of digital sum functions in arbitrary bases**

*Original research paper. Pages 311–318*

Erdenebileg Erdenebat and Ka Lun Wong

Full paper (PDF, 219 Kb) | Abstract

**On some series involving the binomial coefficients **

*Original research paper. Pages 319–334*

Kunle Adegoke, Robert Frontczak and Taras Goy

Full paper (PDF, 280 Kb) | Abstract

**Infinite multisets: Basic properties and cardinality**

*Original research paper. Pages 335–356*

Milen V. Velev

Full paper (PDF, 1.8 Mb) | Abstract

_{0}(the cardinality of the countably infinite set). It has been established that between finite numbers and ℵ

_{0}there exist hierarchies of transfinite m-cardinals, corresponding to infinite msets. Furthermore, there are examples of infinite msets with negative multiplicity that have a cardinality less than zero. We prove that there is a decreasing sequence of transfinite m-cardinal numbers, corresponding to infinite msets with negative multiplicity, and in this sequence, there is not a smallest transfinite m-cardinal number.

**A generalization of arithmetic derivative to p-adic fields and number fields**

*Original research paper. Pages 357–382*

Brad Emmons and Xiao Xiao

Full paper (PDF, 315 Kb) | Abstract

**Melham’s sums for some Lucas polynomial sequences**

*Original research paper. Pages 383–409*

Chan-Liang Chung and Chunmei Zhong

Full paper (PDF, 295 Kb) | Abstract

**On certain bounds for the divisor function**

*Original research paper. Pages 410–417*

József Sándor

Full paper (PDF, 222 Kb) | Abstract

**On certain relations among the generating functions for certain quadratic forms**

*Original research paper. Pages 418–426*

K. R. Vasuki and P. Nagendra

Full paper (PDF, 213 Kb) | Abstract

**On the distribution of powerful and -free lattice points**

*Original research paper. Pages 427–435*

Sunanta Srisopha and Teerapat Srichan

Full paper (PDF, 246 Kb) | Abstract

**On unitary Zumkeller numbers**

*Original research paper. Pages 436–442*

Bhabesh Das

Full paper (PDF, 428 Kb) | Abstract

*n*is a Zumkeller number, then the positive divisors of

*n*can be partitioned into two disjoint subsets of equal sum. Similarly for unitary Zumkeller number

*n*, the unitary divisors of

*n*can be partitioned into two disjoint subsets of equal sum. In this article, we have derived some results related to unitary Zumkeller number, unitary half-Zumkeller number and also presented some numerical examples.

**On tertions and dual numbers**

*Original research paper. Pages 443–452*

Krassimir T. Atanassov

Full paper (PDF, 211 Kb) | Abstract

**Multiplicative Sombor index of trees**

*Original research paper. Pages 453–460*

Nasrin Dehgardi, Zhibin Du and Yilun Shang

Full paper (PDF, 196 Kb) | Abstract

where is the degree of vertex . Liu [Liu, H. (2022). *Discrete Mathematics Letters*, 9, 80–85] showed that, when is a tree of order , . We improved this result and show that, if is a tree of order with maximum degree , then

Also, we show that equality holds if and only if is a spider whose all legs have length less than three or all legs have length more than one.

**Corrigendum to “Two arithmetic functions related to Euler’s and Dedekind’s functions”. [Notes on Number Theory and Discrete Mathematics, 30(1), 179–183]**

*Corrigendum. Pages 461–462*

Krassimir Atanassov

Corrigendum (PDF, 139 Kb)