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Volume 20 (2020)

• A1: A New Class of the r-Stirling Numbers and the Generalized Bernoulli Polynomials
  • Miloud Mihoubi and Meriem Tiachachat
    • PDF Abstract
      DOI: 10.5281/zenodo.10717299

• A2: Jordan's Expansion of the Reciprocal of Theta Functions and 2-densely Divisible Numbers
  • José Manuel Rodríguez Caballero
    • PDF Abstract
      DOI: 10.5281/zenodo.10717323

• A3: The Structure of a Sequence With Prescribed Zero-sum Subsequences
  • David J. Grynkiewicz, Chunlin Wang, and Kevin Zhao
    • PDF Abstract
      DOI: 10.5281/zenodo.10717343

• A4: Shifts of the Prime Divisor Function of Alladi and Erdős
  • Snehal M. Shekatkar and Tian An Wong
    • PDF Abstract
      DOI: 10.5281/zenodo.10717373

• A5: On Generalized Euler Numbers and Polynomials Related to Values of the Lerch Zeta Function
  • Takashi Agoh
    • PDF Abstract
      DOI: 10.5281/zenodo.10717400

• A6: The Distribution of the Generalized Greatest Common Divisor and Visibility of Lattice Points
  • Jorge Flórez, Cihan Karabulut, and Elkin Quintero Vanegas
    • PDF Abstract
      DOI: 10.5281/zenodo.10717425

• A7: Szemerédi-Trotter Type Results in Arbitrary Finite Fields
  • Ali Mohammadi
    • PDF Abstract
      DOI: 10.5281/zenodo.10717435

• A8: A Bijection Between the Triangulations of Convex Polygons and Ordered Trees
  • Dennis E. Davenport, Louis W. Shapiro, and Leon C. Woodson
    • PDF Abstract
      DOI: 10.5281/zenodo.10717441

• A9: Identities and Inequalities for Sums Involving Binomial Coefficients
  • Horst Alzer and Helmut Prodinger
    • PDF Abstract
      DOI: 10.5281/zenodo.10717457

• A10: On the Integrality of Factorial Ratios and Mirror Maps
  • Alan Adolphson and Steven Sperber
    • PDF Abstract
      DOI: 10.5281/zenodo.10717465

• A11: Prime Number Conjectures From the Shapiro Class Structure
  • Hartosh Singh Bal and Gaurav Bhatnagar
    • PDF Abstract
      DOI: 10.5281/zenodo.10717480

• A12: The Combinatorics of Frieze Patterns and Markoff Numbers
  • James Propp
    • PDF Abstract
      DOI: 10.5281/zenodo.10717499

• A13: Diophantine Equations Coming From Binomial Near-collisions
  • Nikos Katsipis
    • PDF Abstract
      DOI: 10.5281/zenodo.10717517

• A14: Some Congruences for (2,5)-regular Cubic Partition Pairs
  • M. S. Mahadeva Naika, Harishkumar T, and Y. Veeranna
    • PDF Abstract
      DOI: 10.5281/zenodo.10776311

• A15: On the Diophantine Equation $\frac{a{x}^{n+2l}+c}{ab{t}^2{x}^n+d}=b{y}^2$
  • Wenyu Luo and Pingzhi Yuan
    • PDF Abstract
      DOI: 10.5281/zenodo.10776321

• A16: Index Divisibility in the Orbit of 0 for Integral Polynomials
  • T. Alden Gassert and Michael T. Urbanski
    • PDF Abstract
      DOI: 10.5281/zenodo.10776327

• A17: Sets of Cardinality 6 Are Not Sum-dominant
  • Hùng Việt Chu
    • PDF Abstract
      DOI: 10.5281/zenodo.10776329

• A18: Partition Inequalities and Applications to Sum-Product Conjectures of Kanade-Russell
  • Walter Bridges
    • PDF Abstract
      DOI: 10.5281/zenodo.10776337

• A19: A Proof of the Infinitude of Primes Via Continued Fractions
  • Joseph Vandehey
    • PDF Abstract
      DOI: 10.5281/zenodo.10776343

• A20: An Euler Phi Function for the Eisenstein Integers and Some Applications
  • Emily Gullerud and aBa Mbirika
    • PDF Abstract
      DOI: 10.5281/zenodo.10776351

• A21: Two New Explicit Formulas for the Bernoulli Numbers
  • Sumit Kumar Jha
    • PDF Abstract
      DOI: 10.5281/zenodo.10776363

• A22: An Improved Exponential Upper Bound for the Erdős-Ginzburg-Ziv Constant
  • Gábor Hegedűs
    • PDF Abstract
      DOI: 10.5281/zenodo.10776375

• A23: On Bivariate and Trivariate Miki-type Identities for Bernoulli Polynomials
  • Takashi Agoh
    • PDF Abstract
      DOI: 10.5281/zenodo.10776379

• A24: Richness of Arithmetic Progressions in Commutative Semigroups
  • Aninda Chakraborty and Sayan Goswami
    • PDF Abstract
      DOI: 10.5281/zenodo.10776396

• A25: Combinatorial Identities Involving Harmonic Numbers
  • Necdet Batır
    • PDF Abstract
      DOI: 10.5281/zenodo.10776457

• A26: Lower and Upper Bounds On Irregularities of Distribution
  • Karl Levy
    • PDF Abstract
      DOI: 10.5281/zenodo.10776466

• A27: A Diophantine System
  • Ajai Choudhry
    • PDF Abstract
      DOI: 10.5281/zenodo.10776476

• A28: Congruences for Overpartition Pairs and 5 Dots Bracelet Partitions Modulo 25
  • Dazhao Tang
    • PDF Abstract
      DOI: 10.5281/zenodo.10776483

• A29: Elliptic Fermat Numbers and Elliptic Divisibility Sequences
  • Seoyoung Kim and Alexandra Walsh
    • PDF Abstract
      DOI: 10.5281/zenodo.10776513

• A30: A Note on Applications from Extending Abel's Lemma
  • Alexander E Patkowski
    • PDF Abstract
      DOI: 10.5281/zenodo.10776519

• A31: Maximal Entries of Elements in Certain Matrix Monoids
  • Sandie Han, Ariane M. Masuda, Satyanand Singh, and Johann Thiel
    • PDF Abstract
      DOI: 10.5281/zenodo.10776528

• A32: Brazilian Primes Which Are Also Sophie Germain Primes
  • Jon Grantham and Hester Graves
    • PDF Abstract
      DOI: 10.5281/zenodo.10776540

• A33: A Characterization of the Sum and Integral Sum Labellings of Some Classes of Graphs
  • Edgar Federico Elizeche and Amitabha Tripathi
    • PDF Abstract
      DOI: 10.5281/zenodo.10776542

• A34: On a Symmetricity Property Connected to the Euclidean Algorithm
  • Srikanth Cherukupally
    • PDF Abstract
      DOI: 10.5281/zenodo.10776552

• A35: Infinite Summation Formulas Involving the Riemann--Zeta Function
  • Xiaoxia Wang and Xueying Yuan
    • PDF Abstract
      DOI: 10.5281/zenodo.10776560

• A36: On the Two-color Rado Number for $x_1+a{x}_2-x_3=c$
  • Srashti Dwivedi and Amitabha Tripathi
    • PDF Abstract
      DOI: 10.5281/zenodo.10776571

• A37: Sums of Powers Over Equally Spaced Fibonacci Numbers
  • Helmut Prodinger
    • PDF Abstract
      DOI: 10.5281/zenodo.10776581

• A38: Congruence Properties for the Trinomial Coefficients
  • Moa Apagodu and Ji-Cai Liu
    • PDF Abstract
      DOI: 10.5281/zenodo.10776589

• A39: Distribution Laws of Friable Divisors
  • S. Nyandwi and A. Smati
    • PDF Abstract
      DOI: 10.5281/zenodo.10776595

• A40: A Note on a Generalization of Fundamental Gaps in Numerical Semigroups
  • Edgar Federico Elizeche and Amitabha Tripathi
    • PDF Abstract
      DOI: 10.5281/zenodo.10776599

• A41: Finite Sums of the Floor Functions Series
  • Ryszard Palka and Zdzislaw Trukszyn
    • PDF Abstract
      DOI: 10.5281/zenodo.10790550

• A42: Generalizations of Wolstenholme's Theorem Via the p-adic Logarithm
  • Peter Lombaers
    • PDF Abstract
      DOI: 10.5281/zenodo.10790541

• A43: A Note on Incomplete Leonardo Numbers
  • P. Catarino and A. Borges
    • PDF Abstract
      DOI: 10.5281/zenodo.10790556

• A44: A Supercongruence Involving Cubes of Catalan Numbers
  • Roberto Tauraso
    • PDF Abstract
      DOI: 10.5281/zenodo.10790565

• A45: The Sum of Digits Function of the Base Phi Expansion of the Natural Numbers
  • Michel Dekking
    • PDF Abstract
      DOI: 10.5281/zenodo.10790571

• A46: On the Finiteness of Carmichael Numbers with Fermat Factors and $L=2^{\alpha }{P}^2$
  • Yu Tsumura
    • PDF Abstract
      DOI: 10.5281/zenodo.10790576

• A47: On Multiplicative Bases of Finite Sets
  • Katalin Fried and Katalin Gyarmati
    • PDF Abstract
      DOI: 10.5281/zenodo.10790580

• A48: Note on a Determinant
  • Benjamin Dupuy
    • PDF Abstract
      DOI: 10.5281/zenodo.10790584

• A49: A Remark on Periods of Periodic Sequences Modulo m
  • Shoji Yokura
    • PDF Abstract
      DOI: 10.5281/zenodo.10790593

• A50: Rainbow Numbers for $x_1+x_2=k{x}_3$ in ${\mathbb{Z}}_n$
  • Erin Bevilacqua, Samuel King, Jürgen Kritschgau, Michael Tait, Suzannah Tebon, and Michael Young
    • PDF Abstract Corrigendum
      DOI: 10.5281/zenodo.10790601

• A51: Rainbow Numbers of ${\mathbb{Z}}_n$ for $a_1{x}_1+a_2{x}_2+a_3{x}_3=b$
  • Katie Ansaldi, Houssein El Turkey, Jessica Hamm, Anisah Nu'Man, Nathan Warnberg, and Michael Young
    • PDF Abstract
      DOI: 10.5281/zenodo.10790604

• A52: Generalized Euler-Genocchi Polynomials and Lucas Numbers
  • Robert Frontczak and Zivorad Tomovski
    • PDF Abstract
      DOI: 10.5281/zenodo.10790609

• A53: On the Averages of Factors of an Infinite Word on a Finite Set of Integers
  • Tom C. Brown and Allen R. Freedman
    • PDF Abstract
      DOI: 10.5281/zenodo.10790617

• A54: An Adaptive Upper Bound on the Ramsey Numbers $R(3,\dots ,3)$
  • Shalom Eliahou
    • PDF Abstract Corrigendum
      DOI: 10.5281/zenodo.10790624

• A55: Families of Non-congruent Numbers With Arbitrarily Many Pairs of Prime Factors
  • Shamik Das and Anupam Saikia
    • PDF Abstract
      DOI: 10.5281/zenodo.10790628

• A56: A Note on a Unitary Analog to Redheffer's Matrix
  • Olivier Bordellès
    • PDF Abstract
      DOI: 10.5281/zenodo.10790640

• A57: The Largest $(k,\ell )$-sum-free Sets in Compact Abelian Groups
  • Noah Kravitz
    • PDF Abstract
      DOI: 10.5281/zenodo.10790634

• A58: Counting Eisenstein Polynomials Satisfying a Condition From Genus Theory
  • Jongwoo Choi and Kevin J. McGown
    • PDF Abstract
      DOI: 10.5281/zenodo.10790646

• A59: Some Identities Involving Central Binomial Coefficients and Catalan Numbers
  • Horst Alzer and Gábor V. Nagy
    • PDF Abstract
      DOI: 10.5281/zenodo.10790650

• A60: An Identity Involving Binomial Coefficients Equivalent to an Identity of Lagrange
  • Hiroshi Ohyama
    • PDF Abstract
      DOI: 10.5281/zenodo.10790652

• A61: Divisor Functions and the Number of Sum Systems
  • Matthew C. Lettington and Karl Michael Schmidt
    • PDF Abstract
      DOI: 10.5281/zenodo.10790658

• A62: Systematic Counting of Restricted Partitions
  • Mingjia Yang and Doron Zeilberger
    • PDF Abstract
      DOI: 10.5281/zenodo.10790664

• A63: On the Theorem of N. P. Romanoff
  • Chadwick Gugg and Andrew Ledoan
    • PDF Abstract
      DOI: 10.5281/zenodo.10790666

• A64: Cartesian Products of Some Combinatorially Rich Sets
  • Sayan Goswami
    • PDF Abstract
      DOI: 10.5281/zenodo.10790668

• A65: Unitary Cyclotomic Polynomials
  • Pieter Moree and László Tóth
    • PDF Abstract
      DOI: 10.5281/zenodo.10790672

• A66: Monochromatic Sums Equal to Products Near Zero
  • Sourav Kanti Patra and Md. Moid Shaikh
    • PDF Abstract
      DOI: 10.5281/zenodo.10790678

• A67: Bernoulli-Stirling Numbers
  • René Gy
    • PDF Abstract
      DOI: 10.5281/zenodo.10790681

• A68: Arithmetical Structures on Paths With a Doubled Edge
  • Darren Glass and Joshua Wagner
    • PDF Abstract
      DOI: 10.5281/zenodo.10792516

• A69: Length of the Continued Logarithm Algorithm on Rational Inputs
  • Jeffrey Shallit
    • PDF Abstract
      DOI: 10.5281/zenodo.10792532

• A70: On the x-coordinates of Pell Equations that are Products of Two Padovan Numbers
  • Mahadi Ddamulira
    • PDF Abstract
      DOI: 10.5281/zenodo.10792535

• A71: 2-adic Properties of Generalized Fibonacci Numbers
  • Paul Thomas Young
    • PDF Abstract
      DOI: 10.5281/zenodo.10792544

• A72: Sum-Products mod m and the Congruence $a{x}_1{x}_2\cdots x_k+b{x}_{k+1}{x}_{k+2}\cdots x_{2k}\equiv c(\mathrm{mod}m)$
  • Todd Cochrane and Sanying Shi
    • PDF Abstract
      DOI: 10.5281/zenodo.10792547

• A73: On the Complete Tree of Primitive Pythagorean Quadruples
  • Jeff Rushall, Marcela Guttierez, and Viola McCarty
    • PDF Abstract
      DOI: 10.5281/zenodo.10792556

• A74: A Note on Some Recent Results of Da Silva and Sellers on Congruences for k-regular Partitions With Designated Summands
  • Nayandeep Deka Baruah and Mandeep Kaur
    • PDF Abstract
      DOI: 10.5281/zenodo.10792563

• A75: On Numerical Semigroups Generated by Primitive Pythagorean Triplets
  • Edgar Federico Elizeche and Amitabha Tripathi
    • PDF Abstract
      DOI: 10.5281/zenodo.10792575

• A76: On Upper Bounds for the Count of Elite Primes
  • Matthew Just
    • PDF Abstract
      DOI: 10.5281/zenodo.10792582

• A77: On a Certain Inverse Problem for Carousel Numbers
  • Katsuya Mori
    • PDF Abstract Errata
      DOI: 10.5281/zenodo.10792595

• A78: A Note on Partitions With Short Profile Steps
  • William J. Keith
    • PDF Abstract
      DOI: 10.5281/zenodo.10792599

• A79: New Congruences Involving Triangular Numbers
  • Xinjie Sun
    • PDF Abstract
      DOI: 10.5281/zenodo.10792602

• A80: Erdős-Kac Theorem for Smooth and Ultra-smooth Integers
  • Marzieh Mehdizadeh
    • PDF Abstract
      DOI: 10.5281/zenodo.10792604

• A81: Numerical Semigroups With Embedding Dimension Three and Minimal Catenary Degree
  • Pedro A. García-Sánchez and Helena Martín Cruz
    • PDF Abstract
      DOI: 10.5281/zenodo.10792612

• A82: Cyclemaster Matrices and Collatz Cycles
  • Stephen M. Zemyan
    • PDF Abstract
      DOI: 10.5281/zenodo.10792630

• A83: On (4, 5)-regular Partitions With Odd Parts Overlined
  • M. S. Mahadeva Naika, Harishkumar T, and T. N. Veeranayaka
    • PDF Abstract
      DOI: 10.5281/zenodo.10792643

• A84: A Graph Theoretic Formula for the Number of Primes π(n)
  • R. Jacobs and C. E. Larson
    • PDF Abstract
      DOI: 10.5281/zenodo.10792647

• A85: Combinatorial Sums and Identities Involving Generalized Sum-of-Divisors Functions with Bounded Divisors
  • Maxie Dion Schmidt
    • PDF Abstract
      DOI: 10.5281/zenodo.10792653

• A86: Lattice Configurations Determining Few Distances
  • Vajresh Balaji, Olivia Edwards, Anne Marie Loftin, Solomon Mcharo, Alex Rice, and Bineyam Tsegaye
    • PDF Abstract
      DOI: 10.5281/zenodo.10792658

• A87: The Union of Two Arithmetic Progressions with the Same Common Difference Is Not Sum-dominant
  • Hùng Việt Chu
    • PDF Abstract
      DOI: 10.5281/zenodo.10802259

• A88: Hyper b-ary Expansions and Stern Polynomials
  • Tanay Wakhare, Caleb Kendrick, Matthew Chung, Catherine Cassell, Stefano Santini, William Colin Mosley, Anand Raghu, Robert Morrison, Iman Schurman, Timothy Kevin Beal, and Matthew Patrick
    • PDF Abstract
      DOI: 10.5281/zenodo.10802263

• A89: Distinct Covering Systems in Number Fields
  • Daniel Baczkowski and Aaron Blodgett
    • PDF Abstract
      DOI: 10.5281/zenodo.10802271

• A90: On the Number of Ordered Factorizations of an Integer
  • Noah Lebowitz-Lockard
    • PDF Abstract
      DOI: 10.5281/zenodo.10802275

• A91: On the Divisibility of Odd Perfect Numbers, Quasiperfect Numbers and Amicable Numbers by a High Power of a Prime
  • Tomohiro Yamada
    • PDF Abstract
      DOI: 10.5281/zenodo.10802277

• A92: A Note on Sums of Two Squares and Sum-of-divisors Functions
  • Mariusz Skałba
    • PDF Abstract
      DOI: 10.5281/zenodo.10802281

• A93: Uniqueness for Sums of Nonvanishing Squares
  • Brian Pigott and Nemanja Kosovalić
    • PDF Abstract
      DOI: 10.5281/zenodo.10802289

• A94: On 5-regular Bipartitions Into Distinct Parts
  • M. Prasad and K. V. Prasad
    • PDF Abstract
      DOI: 10.5281/zenodo.10802291

• A95: On a Conjecture of Victor Guo
  • Slobodan Filipovski and Martin Mačaj
    • PDF Abstract
      DOI: 10.5281/zenodo.10802293

• A96: Crescent Configurations in Normed Spaces
  • Sara Fish, Dylan King, Steven J. Miller, Eyvindur A. Palsson, and Catherine Wahlenmayer
    • PDF Abstract
      DOI: 10.5281/zenodo.10802297

• A97: A Combinatorial Identity for the Sum of Divisors Function Involving $p_r(n)$
  • Sumit Kumar Jha
    • PDF Abstract
      DOI: 10.5281/zenodo.10802300

• A98: Binomial Series Identities Involving Generalized Harmonic Numbers
  • Xiaoyuan Wang and Wenchang Chu
    • PDF Abstract
      DOI: 10.5281/zenodo.10802306

• A99: Binomial Probability of Prime Number of Successes
  • Sungjin Kim and Nilotpal Kanti Sinha
    • PDF Abstract
      DOI: 10.5281/zenodo.10802308

• A100: Linear Combinations of Two Polygonal Numbers That Take Infinitely Often a Square Value
  • Yangcheng Li
    • PDF Abstract
      DOI: 10.5281/zenodo.10802310

• A101: A Family of Partitions Equinumerous With the Set of Nodes of a Family of Trees
  • Hemar Godinho and José Plínio O. Santos
    • PDF Abstract
      DOI: 10.5281/zenodo.10802314

• A102: Ulam Sets in New Settings
  • Tej Bade, Kelly Cui, Antoine Labelle, and Deyuan Li
    • PDF Abstract
      DOI: 10.5281/zenodo.10802318

• A103: An Improved Inequality of Rosser and Schoenfled and Its Application
  • Shaohua Zhang
    • PDF Abstract
      DOI: 10.5281/zenodo.10802324

• A104: On the Monotonicity of Additive Representation Functions
  • Pascal Stumpf
    • PDF Abstract
      DOI: 10.5281/zenodo.10802326

• A105: Generalized Fibonacci Numbers and Their 2-adic Order
  • Martin Bunder and Joseph Tonien
    • PDF Abstract
      DOI: 10.5281/zenodo.10802328

• A106: Total Positivity of Toeplitz Matrices of Hyperlucas Sequence
  • Boualam Rezig and Moussa Ahmia
    • PDF Abstract
      DOI: 10.5281/zenodo.10802333

Games Articles

• G1: Grundy Numbers of Impartial Chocolate Bar Games
  • Ryohei Miyadera, Shunsuke Nakamura, and Yushi Nakaya
    • PDF Abstract
      DOI: 10.5281/zenodo.10802337

• G2: Atomic Weight Calculus of Spindly Games
  • Michael Fisher, Neil McKay, Richard J. Nowakowski, Paul Ottaway, and Carlos Pereira dos Santos
    • PDF Abstract
      DOI: 10.5281/zenodo.10802339

• G3: Slow k-Nim
  • Vladimir Gurvich, Silvia Heubach, Hhan Bao Ho, and Nikolay Chikin
    • PDF Abstract
      DOI: 10.5281/zenodo.10802345

• G4: The Sprague-Grundy Function for Some Selective Compound Games
  • Calvin Beideman, Matthew Bowen, and Alp Müyesser
    • PDF Abstract
      DOI: 10.5281/zenodo.10802351

• G5: The Periodicity of Nim-Sequences in Two-Element Subtraction Games
  • Bret Benesh, Jamylle Carter, Doug Crabill, Deidra Coleman, Jack Good, Michael Smith, Jennifer Travis, and Mark Daniel Ward
    • PDF Abstract
      DOI: 10.5281/zenodo.10802357

• G6: A Note on a Subtraction--Transfer Game
  • Tamás Lengyel
    • PDF Abstract
      DOI: 10.5281/zenodo.10802369

• G7: An Achievement Game on a Cycle
  • Eero Räty
    • PDF Abstract
      DOI: 10.5281/zenodo.10802371

• G8: The Self-Referential Impartial Game Minnie
  • Todd Mullen and Richard Nowakowski
    • PDF Abstract
      DOI: 10.5281/zenodo.10802373

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