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Volume 21 (2021)

• A1: Infinite Series Containing Generalized q-harmonic Numbers
  • Takao Komatsu and Rusen Li
    • PDF Abstract
      DOI: 10.5281/zenodo.10803329

• A2: On the Symmetry Graph of Prime Numbers
  • A. B. Kalmynin
    • PDF Abstract
      DOI: 10.5281/zenodo.10803335

• A3: A Method for Generating Permutation Polynomials Modulo pⁿ
  • Rajesh P. Singh
    • PDF Abstract
      DOI: 10.5281/zenodo.10803345

• A4: The South Caicos Factoring Algorithm
  • Michael O. Rubinstein
    • PDF Abstract
      DOI: 10.5281/zenodo.10803351

• A5: Congruences for Certain Lacunary Sums of Products of Binomial Coefficients
  • René Gy
    • PDF Abstract
      DOI: 10.5281/zenodo.10803355

• A6: The Structure of Zeckendorf Expansions
  • F. Michel Dekking
    • PDF Abstract
      DOI: 10.5281/zenodo.10803363

• A7: Balancing and Lucas-balancing Numbers Expressible as Sums of Two Repdigits
  • Sai Gopal Rayaguru and Gopal Krishna Panda
    • PDF Abstract
      DOI: 10.5281/zenodo.10803367

• A8: On the Minimum Cardinality of Generalized Sumsets in Finite Cyclic Groups
  • Jagannath Bhanja
    • PDF Abstract
      DOI: 10.5281/zenodo.10803370

• A9: Congruences For Fractional Partition Functions
  • Yunseo Choi
    • PDF Abstract
      DOI: 10.5281/zenodo.10803375

• A10: On Numerical Semigroups Generated by Compound Sequences
  • Amitabha Tripathi
    • PDF Abstract
      DOI: 10.5281/zenodo.10803378

• A11: The Factorial Moments of the Generalized Bernoulli-Fibonacci Distribution
  • Petros Hadjicostas
    • PDF Abstract
      DOI: 10.5281/zenodo.10803388

• A12: Multivariable Lucas Polynomials and Lucanomials
  • Edward E. Allen, Katherine Riley, and Michael Weselcouch
    • PDF Abstract
      DOI: 10.5281/zenodo.10803436

• A13: Alternative Formulations of the Generalized Cosecand and Secant Numbers
  • Victor Kowalenko
    • PDF Abstract
      DOI: 10.5281/zenodo.10803464

• A14: Invariant Measures for 2-dimensional Maps and Associated Rényi Maps
  • Fritz Schweiger
    • PDF Abstract
      DOI: 10.5281/zenodo.10807484

• A15: Some Congruences for (s,t)-regular Bipartitions Modulo t
  • T. Kathiravan and K. Srilakshmi
    • PDF Abstract
      DOI: 10.5281/zenodo.10807496

• A16: Walking to Infinity Along Gaussian Lines
  • Elsa Magness, Brian Nugent, and Leanne Robertson
    • PDF Abstract
      DOI: 10.5281/zenodo.10807500

• A17: The Frobenius Problem for Extended Thabit Numerical Semigroups
  • Kyunghwan Song
    • PDF Abstract
      DOI: 10.5281/zenodo.10807506

• A18: On the Family of Elliptic Curves \(X + 1/X + Y + 1/Y + t = 0\)
  • Abhishek Juyal and Dustin Moody
    • PDF Abstract
      DOI: 10.5281/zenodo.10807511

• A19: Exact Formulas for the Generalized Sum-of-Divisors Functions
  • Maxie Dion Schmidt
    • PDF Abstract
      DOI: 10.5281/zenodo.10807515

• A20: Lucas Congruences for the Apéry Numbers Modulo p²
  • Eric Rowland, Reem Yassawi, and Christian Krattenthaler
    • PDF Abstract
      DOI: 10.5281/zenodo.10807517

• A21: Quotients of Hurwitz Primes
  • Minghao Pan and Wentao Zhang
    • PDF Abstract
      DOI: 10.5281/zenodo.10807521

• A22: Some Nested Sums in Terms of the Riemann Zeta Function and the Dirichlet Beta Function
  • Sumit Kumar Jha
    • PDF Abstract
      DOI: 10.5281/zenodo.10807527

• A23: Dirichlet Series with Trigonometric Coefficients
  • Johann Franke
    • PDF Abstract
      DOI: 10.5281/zenodo.10807533

• A24: A Note on the Erdős-Straus Conjecture
  • Kyle Bradford
    • PDF Abstract
      DOI: 10.5281/zenodo.10807535

• A25: Isomorphism Classes of Distance Graphs in \(\mathbb{Q}^3\)
  • Matt Noble
    • PDF Abstract
      DOI: 10.5281/zenodo.10807539

• A26: Extensions of Midy's Theorem for Periodic Decimals
  • Sakshi Dang, Saraswati Nanoti, and Amitabha Tripathi
    • PDF Abstract
      DOI: 10.5281/zenodo.10807543

• A27: The Number of Optimal Strategies in the Penney-Ante Game
  • Reed Phillips and A.J. Hildebrand
    • PDF Abstract
      DOI: 10.5281/zenodo.10807551

• A28: Robin's Inequality for 20-free Integers
  • Thomas Morrill and David John Platt
    • PDF Abstract
      DOI: 10.5281/zenodo.10807556

• A29: The Bi-periodic Fibonacci-Horadam Matrix
  • Joy P. Ascaño and Edna N. Gueco
    • PDF Abstract
      DOI: 10.5281/zenodo.10807568

• A30: Shifted Convolution Sums of Arithmetic Functions of Two Variables and Ramanujan Expansions
  • Noboru Ushiroya
    • PDF Abstract
      DOI: 10.5281/zenodo.10807572

• A31: Harmonic Numbers and the Prime Counting Function
  • Jesse Elliott
    • PDF Abstract
      DOI: 10.5281/zenodo.10807579

• A32: A Recurring Pattern in Natural Numbers of a Certain Property
  • Daniel Tsai
    • PDF Abstract
      DOI: 10.5281/zenodo.10807581

• A33: Complete Additivity, Complete Multiplicativity, and Leibniz-additivity on Rationals
  • Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen
    • PDF Abstract
      DOI: 10.5281/zenodo.10807583

• A34: Repetitions of Multinomial Coefficients and a Generalization of Singmaster's Conjecture
  • Jean-Marie de Koninck, Nicolas Doyon, and William Verreault
    • PDF Abstract
      DOI: 10.5281/zenodo.10807587

• A35: An Analogue of k-marked Durfee Symbols for Strongly Unimodal Sequences
  • Savana Ammons, Young Jin Kim, Laura Seaberg, and Holly Swisher
    • PDF Abstract
      DOI: 10.5281/zenodo.10816743

• A36: Abelian Complexity and Synchronization
  • Jeffrey Shallit
    • PDF Abstract
      DOI: 10.5281/zenodo.10816751

• A37: The Mondrian Puzzle: A Bound Concerning the M(n)=0 Case
  • Cooper O'Kuhn and Todd Fellman
    • PDF Abstract
      DOI: 10.5281/zenodo.10816755

• A38: On Third-order Pell Polynomials
  • Helmut Prodinger
    • PDF Abstract
      DOI: 10.5281/zenodo.10816761

• A39: A Sextic Diophantine Chain and a Related Mordell Curve
  • Ajai Choudhry and Arman Shamsi Zargar
    • PDF Abstract
      DOI: 10.5281/zenodo.10816767

• A40: Cyclotomic Points and Algebraic Properties of Polygon Diagonals
  • Thomas Grubb and Christian Wolird
    • PDF Abstract
      DOI: 10.5281/zenodo.10816775

• A41: The Number of Parts in the (Distinct) Partitions with Parts From a Set
  • A. David Christopher
    • PDF Abstract
      DOI: 10.5281/zenodo.10816778

• A42: A New Property of Appell Sequences and Its Application
  • Takashi Agoh
    • PDF Abstract
      DOI: 10.5281/zenodo.10816788

• A43: Uniqueness of Optimal Point Sets Determining Two Distinct Triangles
  • Hazel N. Brenner, James S. Depret-Guillaume, Eyvindur A. Palsson, and Steven Senger
    • PDF Abstract
      DOI: 10.5281/zenodo.10816792

• A44: From a Hungary-Israel Contest Problem
  • Fang Chen
    • PDF Abstract
      DOI: 10.5281/zenodo.10816798

• A45: Discrete Correlations of Order 2 of Generalized Golay-Shapiro Sequences: A Combinatorial Approach
  • Irène Marcovici, Thomas Stoll, and Pierre-Adrien Tahay
    • PDF Abstract
      DOI: 10.5281/zenodo.10816802

• A46: The Abelian Complexity of Infinite Words and the Frobenius Problem
  • Ian Kaye and Narad Rampersad
    • PDF Abstract
      DOI: 10.5281/zenodo.10816807

• A47: Evaluation of Convolution Sums Involving Cubic Divisor Functions for a Class of Levels
  • Ebénézer Ntienjem
    • PDF Abstract
      DOI: 10.5281/zenodo.10816811

• A48: On a Generalized Family of Euler-Genocchi Polynomials
  • Mouloud Goubi
    • PDF Abstract
      DOI: 10.5281/zenodo.10816818

• A49: On Certain Diophantine Equations Involving Triangular Numbers
  • Junyao Peng and Yong Zhang
    • PDF Abstract
      DOI: 10.5281/zenodo.10816820

• A50: Perron Numbers and Positive Matrices of Minimal Order
  • Anne Bertrand-Mathis and Florent Nguema Ndong
    • PDF Abstract
      DOI: 10.5281/zenodo.10816822

• A51: On the Directions Determined by Cartesian Products and the Clique Number of Generalized Paley Graphs
  • Chi Hoi Yip
    • PDF Abstract
      DOI: 10.5281/zenodo.10816828

• A52: On Carmichael and Polygonal Numbers, Bernoulli Polynomials, and Sums of Base-p Digits
  • Bernd C. Kellner and Jonathan Sondow
    • PDF Abstract
      DOI: 10.5281/zenodo.10816833

• A53: Carleman's Inequality Over Prime Numbers
  • Christian Axler and Mehdi Hassani
    • PDF Abstract
      DOI: 10.5281/zenodo.10816841

• A54: A Generalization of the Kővári--Sós--Turán Theorem
  • Jesse Geneson
    • PDF Abstract
      DOI: 10.5281/zenodo.10816844

• A55: Distinct Distances From Points on a Circle to a Generic Set
  • Alex McDonald, Brian McDonald, Jonathan Passant, and Anurag Sahay
    • PDF Abstract
      DOI: 10.5281/zenodo.10816846

• A56: Sums and Convolutions of k-bonacci and k-Lucas Numbers
  • Greg Dresden and Yichen Wang
    • PDF Abstract
      DOI: 10.5281/zenodo.10816848

• A57: Particular Pell-Fermat Equations Revisited
  • Antoine Mhanna
    • PDF Abstract
      DOI: 10.5281/zenodo.10816850

• A58: On the Sum of Two Squares and at Most k Powers of 2
  • Dan Wang
    • PDF Abstract
      DOI: 10.5281/zenodo.10816856

• A59: New Lower Bounds for Weak Schur Partitions
  • Fred Rowley
    • PDF Abstract
      DOI: 10.5281/zenodo.10816866

• A60: Explicit Expressions for a Certain Subset of Appell Polynomials: A Probabilistic Perspective
  • José A. Adell and Alberto Lekuona
    • PDF Abstract
      DOI: 10.5281/zenodo.10816868

• A61: On Binomial Coefficients Associated with Sierpiński and Riesel Numbers
  • Ashley Armbruster, Grace Barger, Sofya Bykova, Tyler Dvoracheck, Emily Eckard, Joshua Harrington, Yewen Sun, and Tony W. H. Wong
    • PDF Abstract
      DOI: 10.5281/zenodo.10817556

• A62: Finite Sums of Arithmetic Progressions
  • Shahram Mohsenipour
    • PDF Abstract
      DOI: 10.5281/zenodo.10817562

• A63: Newton Sequences and Dirichlet Convolution
  • Klaudiusz Klaudiusz Wójcik
    • PDF Abstract
      DOI: 10.5281/zenodo.10817568

• A64: Note on a Determinant (II)
  • Benjamin Dupuy
    • PDF Abstract
      DOI: 10.5281/zenodo.10817573

• A65: Proper Divisor Graph of a Positive Integer
  • Hitesh Kumar, Kamal Lochan Patra, and Binod Kumar Sahoo
    • PDF Abstract
      DOI: 10.5281/zenodo.10817582

• A66: A Generalization of Selfridge's Question
  • Devendra Prasad
    • PDF Abstract
      DOI: 10.5281/zenodo.10817586

• A67: On the Frobenius Conjecture
  • Mélodie Lapointe and Christophe Reutenauer
    • PDF Abstract
      DOI: 10.5281/zenodo.10817590

• A68: On the Equation φ(n+k)=2φ(n)
  • Elchin Hasanalizade
    • PDF Abstract
      DOI: 10.5281/zenodo.10817596

• A69: Enumerating Restricted Dyck Paths with Context Free Grammars
  • AJ Bu and Robert Dougherty-Bliss
    • PDF Abstract
      DOI: 10.5281/zenodo.10817600

• A70: On the Prime Factors of Φ_p(M)
  • Luis H. Gallardo
    • PDF Abstract
      DOI: 10.5281/zenodo.10817604

• A71: Hausdorff Dimension of Sets of Numbers with Large Lüroth Elements
  • Aubin Arroyo and Gerardo González Robert
    • PDF Abstract
      DOI: 10.5281/zenodo.10834754

• A72: A Combinatorial Viewpoint on Preserving Notions of Largeness and an Abstract Rado Theorem
  • Sayan Goswami and Subhajit Jana
    • PDF Abstract
      DOI: 10.5281/zenodo.10834758

• A73: Linear Recurrences for Bernoulli Polynomials Involving Different Kinds of Sums
  • Takashi Agoh
    • PDF Abstract
      DOI: 10.5281/zenodo.10834765

• A74: An Elementary Computer Assisted Unique Factorization Test
  • Sándor Szabó
    • PDF Abstract
      DOI: 10.5281/zenodo.10834767

• A75: A Bijection Between Two Different Classes of Partitions Enumerated by p_ν(n)
  • A.S. Andersen
    • PDF Abstract
      DOI: 10.5281/zenodo.10834771

• A76: On the Total Number of Prime Factors of an Odd Perfect Number
  • Joshua Zelinsky
    • PDF Abstract
      DOI: 10.5281/zenodo.10834776

• A77: Algebraic Properties of a Hypergraph Lifting Map
  • Mark Budden, Josh Hiller, Tommy Meek, and Andrew Penland
    • PDF Abstract
      DOI: 10.5281/zenodo.10834780

• A78: On the Combinatorics of Placing Balls into Ordered Bins
  • Vedant Bonde and Joshua M. Siktar
    • PDF Abstract
      DOI: 10.5281/zenodo.10834788

• A79: On Sets Whose Subsets Have Integer Mean
  • Enrique Treviño
    • PDF Abstract
      DOI: 10.5281/zenodo.10834794

• A80: Weighted Partitions and Generalized r-Lah Numbers
  • Hacène Belbachir, Amine Belkhir, and Imad-Eddine Bousbaa
    • PDF Abstract
      DOI: 10.5281/zenodo.10834796

• A81: The Natural Density of Some Sets of Square-free Numbers
  • Ron Brown
    • PDF Abstract
      DOI: 10.5281/zenodo.10834803

• A82: A Formula for the Number of Overpartitions of n in Terms of the Number of Representations of n as a Sum of r Squares
  • Sumit Kumar Jha
    • PDF Abstract
      DOI: 10.5281/zenodo.10834805

• A83: The n-color Partition Function and Some Counting Theorems
  • Subhajit Bandyopadhyay and Nayandeep Deka Baruah
    • PDF Abstract
      DOI: 10.5281/zenodo.10834807

• A84: On Representations of the Riemann Zeta Function, Its Square and of the Positive Integers
  • Urpo M. Kyllönen
    • PDF Abstract Errata
      DOI: 10.5281/zenodo.10834817

• A85: Parity Palindrome Compositions
  • George E. Andrews and Greg Simay
    • PDF Abstract
      DOI: 10.5281/zenodo.10834827

• A86: On Some p-adic Properties and Supercongruences of Delannoy and Schröder Numbers
  • Tamás Lengyel
    • PDF Abstract
      DOI: 10.5281/zenodo.10834839

• A87: Exceptional Totient Numbers
  • Breille Duncan, Joshua Harrington, and Andrew Vincent
    • PDF Abstract
      DOI: 10.5281/zenodo.10834847

• A88: Will the Real Hardy--Ramanujan Formula Please Stand Up?
  • Stephen DeSalvo
    • PDF Abstract
      DOI: 10.5281/zenodo.10834852

• A89: Arithmetic Subsequences in a Random Ordering of an Additive Set
  • Marcel K. Goh and Rosie Y. Zhao
    • PDF Abstract
      DOI: 10.5281/zenodo.10834856

• A90: Geometric Patterns in The Determinant Hosoya Triangle
  • Matthew Blair, Rigoberto Flórez, and Antara Mukherjee
    • PDF Abstract
      DOI: 10.5281/zenodo.10834860

• A91: Fibonacci Colored Compositions and Applications
  • Juan B. Gil and Jessica A. Tomasko
    • PDF Abstract
      DOI: 10.5281/zenodo.10834864

• A92: Algorithms for the Multiplication Table Problem
  • Richard Brent, Carl Pomerance, David Purdum, and Jonathan Webster
    • PDF Abstract
      DOI: 10.5281/zenodo.10834870

• A93: Small Solutions of \(ax_1\cdots x_k + bx_{k+1}\cdots x_{2k} \equiv c \pmod{m}\) under the Lindelöf Hypothesis
  • Todd Cochrane and Sanying Shi
    • PDF Abstract
      DOI: 10.5281/zenodo.10834877

• A94: Sums over Primes
  • Rusen Li
    • PDF Abstract
      DOI: 10.5281/zenodo.10834893

• A95: Recurrence Relations for Generalized Laguerre Polynomials
  • Takashi Agoh
    • PDF Abstract
      DOI: 10.5281/zenodo.10834917

• A96: Extrema of Luroth Digits and a Zeta Function Limit Relation
  • Jayadev S. Athreya and Krishna B. Athreya
    • PDF Abstract
      DOI: 10.5281/zenodo.10834930

• A97: Maximum Distances in the Four-digit Kaprekar Process
  • Pat Devlin and Tony Zeng
    • PDF Abstract
      DOI: 10.5281/zenodo.10839316

• A98: On the Equality of Dedekind Sums
  • Kurt Girstmair
    • PDF Abstract
      DOI: 10.5281/zenodo.10839330

• A99: Representation Numbers of Spinor Regular Ternary Quadratic Forms
  • Zafer Selcuk Aygin, Greg Doyle, Florian Münkel, Lerna Pehlivan, and Kenneth S. Williams
    • PDF Abstract
      DOI: 10.5281/zenodo.10839340

• A100: Chebyshev-Fibonacci Polynomial Relations Using Generating Functions
  • Robert Frontczak and Taras Goy
    • PDF Abstract
      DOI: 10.5281/zenodo.10839350

• A101: High Degree b-Niven Numbers
  • Viorel Nitica
    • PDF Abstract
      DOI: 10.5281/zenodo.10839362

• A102: Values of Weighted Davenport Constants
  • Rene Ardila, Christine Caples, Helen G. Grundman, Laura L. Hall-Seelig, Jill E. Jordan, Karen T. Kohl, and Thomas P. Wakefield
    • PDF Abstract
      DOI: 10.5281/zenodo.10839373

• A103: Three Imprimitive Character Sums
  • Brad Isaacson
    • PDF Abstract
      DOI: 10.5281/zenodo.10839389

• A104: Multidimensional Small Divisor Functions
  • Andreas Mono
    • PDF Abstract
      DOI: 10.5281/zenodo.10839396

• A105: Abundance of Arithmetic Progressions in Some Combinatorially Rich Sets by Elementary Means
  • Pintu Debnath and Sayan Goswami
    • PDF Abstract
      DOI: 10.5281/zenodo.10839408

• A106: On (Yet Another) Family of Stirling Polynomials of the Second Kind
  • Helena Cobo
    • PDF Abstract
      DOI: 10.5281/zenodo.10839433

• A107: WZ Proofs for Lemniscate-like Constant Evaluations
  • John Maxwell Campbell
    • PDF Abstract
      DOI: 10.5281/zenodo.10839443

• A108: On Pillai's Problem with Lucas Numbers and Powers of 3
  • Bilizimbéyé Edjeou, Amadou Tall, and Mohamed Ben Fraj Ben Maaouia
    • PDF Abstract
      DOI: 10.5281/zenodo.10839449

• A109: Lucas-Lehmer Primality Tests for Certain Prime Curios
  • E. L. Roettger and H. C. Williams
    • PDF Abstract
      DOI: 10.5281/zenodo.10839461

• A110: Some Diophantine Problems Concerning a Pair of Rational Triangles with a Common Circumradius
  • Ajai Choudhry
    • PDF Abstract
      DOI: 10.5281/zenodo.10839470

• A111: Proof of Two Conjectures of Andrica and Bagdasar
  • Jon Grantham
    • PDF Abstract
      DOI: 10.5281/zenodo.10839483

• A112: Gibonacci Polynomial Products with Implications
  • Thomas Koshy
    • PDF Abstract
      DOI: 10.5281/zenodo.10839488

• A113: Multiplicative Functions with \(f(p+q-n_0) = f(p)+f(q)-f(n_0)\)
  • Poo-Sung Park
    • PDF Abstract
      DOI: 10.5281/zenodo.10842298

• A114: Finite Sums of Consecutive Terms of a Second Order Linear Recurrence Relation
  • Curtis Cooper
    • PDF Abstract
      DOI: 10.5281/zenodo.10842307

• A115: On the Third Largest Prime Divisor of an Odd Perfect Number
  • Sean Bibby, Pieter Vyncke, and Joshua Zelinsky
    • PDF Abstract
      DOI: 10.5281/zenodo.10842315

• A116: Binary Recurrences with Prime Powers as Fixed Points of Their Discriminator
  • Matteo Ferrari
    • PDF Abstract
      DOI: 10.5281/zenodo.10842319

• A117: On Solutions to Erdős' Last Equation
  • Wataru Takeda
    • PDF Abstract
      DOI: 10.5281/zenodo.10842321

• A118: Polynomial Interpolation of Modular Forms for Hecke Groups
  • Barry Brent
    • PDF Abstract
      DOI: 10.5281/zenodo.10842324

• A119: On (Self-) Reciprocal Appell Polynomials: Symmetry and Faulhaber-type Polynomials
  • Bernd C. Kellner
    • PDF Abstract
      DOI: 10.5281/zenodo.10842328

• A120: Higher Degree Davenport Constants over Finite Commutative Rings
  • Yair Caro, Benjamin Girard, and John R. Schmitt
    • PDF Abstract
      DOI: 10.5281/zenodo.10842330

• A121: A New Class of Polynomials Related to the Stirling Numbers and Series Representations for Some Mathematical Constants
  • Horst Alzer and Emanuele Munarini
    • PDF Abstract
      DOI: 10.5281/zenodo.10842332

• A122: On the Counting Function of Semiprimes
  • Dragoș Crișan and Radek Erban
    • PDF Abstract
      DOI: 10.5281/zenodo.10842336

• A123: A Note on Integers That Are Uniquely Expressible by Integral Geometric Sequences
  • Edgar Federico Elizeche and Amitabha Tripathi
    • PDF Abstract
      DOI: 10.5281/zenodo.10842338

• A124: Frobenius Numbers and Automatic Sequences
  • Jeffrey Shallit
    • PDF Abstract
      DOI: 10.5281/zenodo.10842348

Games Articles

• G1: A Codex of N- and P-positions in Harary's 'Caterpillar Game'
  • Richard M. Low, Ardak Kapbasov, Arman Kapbasov, Stephen C. Locke, and W. H. Chan
    • PDF Abstract
      DOI: 10.5281/zenodo.10842672

• G2: Amalgamation Nim
  • S.C. Locke and B. Handley
    • PDF Abstract
      DOI: 10.5281/zenodo.10842684

• G3: On the Additive Period Length of the Sprague-Grundy Function of Certain Nim-like Games
  • Jens Askgaard
    • PDF Abstract
      DOI: 10.5281/zenodo.10842693

• G4: More about Exact Slow k-Nim
  • Nikolay Chikin, Vladimir Gurvich, Konstantin Knop, Mike Paterson, and Michael Vyalyi
    • PDF Abstract
      DOI: 10.5281/zenodo.10842707

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