Volume 21 (2021)
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A1:
Infinite Series Containing Generalized q-harmonic Numbers
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Takao Komatsu and Rusen Li
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A2:
On the Symmetry Graph of Prime Numbers
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A3:
A Method for Generating Permutation Polynomials Modulo pn
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A4:
The South Caicos Factoring Algorithm
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A5:
Congruences for Certain Lacunary Sums of Products of Binomial Coefficients
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A6:
The Structure of Zeckendorf Expansions
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A7:
Balancing and Lucas-balancing Numbers Expressible as Sums of Two Repdigits
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Sai Gopal Rayaguru and Gopal Krishna Panda
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A8:
On the Minimum Cardinality of Generalized Sumsets in Finite Cyclic Groups
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A9:
Congruences For Fractional Partition Functions
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A10:
On Numerical Semigroups Generated by Compound Sequences
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A11:
The Factorial Moments of the Generalized Bernoulli-Fibonacci Distribution
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A12:
Multivariable Lucas Polynomials and Lucanomials
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Edward E. Allen, Katherine Riley, and Michael Weselcouch
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A13:
Alternative Formulations of the Generalized Cosecand and Secant Numbers
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A14:
Invariant Measures for 2-dimensional Maps and Associated Rényi Maps
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A15:
Some Congruences for (s,t)-regular Bipartitions Modulo t
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T. Kathiravan and K. Srilakshmi
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A16:
Walking to Infinity Along Gaussian Lines
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Elsa Magness, Brian Nugent, and Leanne Robertson
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A17:
The Frobenius Problem for Extended Thabit Numerical Semigroups
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A18:
On the Family of Elliptic Curves \(X + 1/X + Y + 1/Y + t = 0\)
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Abhishek Juyal and Dustin Moody
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A19:
Exact Formulas for the Generalized Sum-of-Divisors Functions
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A20:
Lucas Congruences for the Apéry Numbers Modulo p2
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Eric Rowland, Reem Yassawi, and Christian Krattenthaler
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A21:
Quotients of Hurwitz Primes
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Minghao Pan and Wentao Zhang
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A22:
Some Nested Sums in Terms of the Riemann Zeta Function and the Dirichlet Beta Function
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A23:
Dirichlet Series with Trigonometric Coefficients
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A24:
A Note on the Erdős-Straus Conjecture
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A25:
Isomorphism Classes of Distance Graphs in \(\mathbb{Q}^3\)
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A26:
Extensions of Midy's Theorem for Periodic Decimals
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Sakshi Dang, Saraswati Nanoti, and Amitabha Tripathi
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A27:
The Number of Optimal Strategies in the Penney-Ante Game
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Reed Phillips and A.J. Hildebrand
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A28:
Robin's Inequality for 20-free Integers
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Thomas Morrill and David John Platt
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A29:
The Bi-periodic Fibonacci-Horadam Matrix
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Joy P. Ascaño and Edna N. Gueco
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A30:
Shifted Convolution Sums of Arithmetic Functions of Two Variables and Ramanujan Expansions
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A31:
Harmonic Numbers and the Prime Counting Function
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A32:
A Recurring Pattern in Natural Numbers of a Certain Property
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A33:
Complete Additivity, Complete Multiplicativity, and Leibniz-additivity on Rationals
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Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen
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A34:
Repetitions of Multinomial Coefficients and a Generalization of Singmaster's Conjecture
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Jean-Marie de Koninck, Nicolas Doyon, and William Verreault
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A35:
An Analogue of k-marked Durfee Symbols for Strongly Unimodal Sequences
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Savana Ammons, Young Jin Kim, Laura Seaberg, and Holly Swisher
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A36:
Abelian Complexity and Synchronization
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A37:
The Mondrian Puzzle: A Bound Concerning the M(n)=0 Case
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Cooper O'Kuhn and Todd Fellman
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A38:
On Third-order Pell Polynomials
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A39:
A Sextic Diophantine Chain and a Related Mordell Curve
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Ajai Choudhry and Arman Shamsi Zargar
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A40:
Cyclotomic Points and Algebraic Properties of Polygon Diagonals
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Thomas Grubb and Christian Wolird
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A41:
The Number of Parts in the (Distinct) Partitions with Parts From a Set
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A42:
A New Property of Appell Sequences and Its Application
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A43:
Uniqueness of Optimal Point Sets Determining Two Distinct Triangles
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Hazel N. Brenner, James S. Depret-Guillaume, Eyvindur A. Palsson, and Steven Senger
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A44:
From a Hungary-Israel Contest Problem
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A45:
Discrete Correlations of Order 2 of Generalized Golay-Shapiro Sequences: A Combinatorial Approach
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Irène Marcovici, Thomas Stoll, and Pierre-Adrien Tahay
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A46:
The Abelian Complexity of Infinite Words and the Frobenius Problem
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Ian Kaye and Narad Rampersad
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A47:
Evaluation of Convolution Sums Involving Cubic Divisor Functions for a Class of Levels
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A48:
On a Generalized Family of Euler-Genocchi Polynomials
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A49:
On Certain Diophantine Equations Involving Triangular Numbers
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Junyao Peng and Yong Zhang
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A50:
Perron Numbers and Positive Matrices of Minimal Order
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Anne Bertrand-Mathis and Florent Nguema Ndong
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A51:
On the Directions Determined by Cartesian Products and the Clique Number of Generalized Paley Graphs
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A52:
On Carmichael and Polygonal Numbers, Bernoulli Polynomials, and Sums of Base-p Digits
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Bernd C. Kellner and Jonathan Sondow
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A53:
Carleman's Inequality Over Prime Numbers
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Christian Axler and Mehdi Hassani
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A54:
A Generalization of the Kővári--Sós--Turán Theorem
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A55:
Distinct Distances From Points on a Circle to a Generic Set
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Alex McDonald, Brian McDonald, Jonathan Passant, and Anurag Sahay
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A56:
Sums and Convolutions of k-bonacci and k-Lucas Numbers
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Greg Dresden and Yichen Wang
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A57:
Particular Pell-Fermat Equations Revisited
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A58:
On the Sum of Two Squares and at Most k Powers of 2
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A59:
New Lower Bounds for Weak Schur Partitions
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A60:
Explicit Expressions for a Certain Subset of Appell Polynomials: A Probabilistic Perspective
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José A. Adell and Alberto Lekuona
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A61:
On Binomial Coefficients Associated with Sierpiński and Riesel Numbers
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Ashley Armbruster, Grace Barger, Sofya Bykova, Tyler Dvoracheck, Emily Eckard, Joshua Harrington, Yewen Sun, and Tony W. H. Wong
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A62:
Finite Sums of Arithmetic Progressions
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A63:
Newton Sequences and Dirichlet Convolution
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Klaudiusz Klaudiusz Wójcik
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A64:
Note on a Determinant (II)
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A65:
Proper Divisor Graph of a Positive Integer
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Hitesh Kumar, Kamal Lochan Patra, and Binod Kumar Sahoo
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A66:
A Generalization of Selfridge's Question
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A67:
On the Frobenius Conjecture
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Mélodie Lapointe and Christophe Reutenauer
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A68:
On the Equation φ(n+k)=2φ(n)
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A69:
Enumerating Restricted Dyck Paths with Context Free Grammars
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AJ Bu and Robert Dougherty-Bliss
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A70:
On the Prime Factors of Φp(M)
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A71:
Hausdorff Dimension of Sets of Numbers with Large Lüroth Elements
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Aubin Arroyo and Gerardo González Robert
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A72:
A Combinatorial Viewpoint on Preserving Notions of Largeness and an Abstract Rado Theorem
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Sayan Goswami and Subhajit Jana
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A73:
Linear Recurrences for Bernoulli Polynomials Involving Different Kinds of Sums
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A74:
An Elementary Computer Assisted Unique Factorization Test
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A75:
A Bijection Between Two Different Classes of Partitions Enumerated by pν(n)
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A76:
On the Total Number of Prime Factors of an Odd Perfect Number
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A77:
Algebraic Properties of a Hypergraph Lifting Map
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Mark Budden, Josh Hiller, Tommy Meek, and Andrew Penland
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A78:
On the Combinatorics of Placing Balls into Ordered Bins
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Vedant Bonde and Joshua M. Siktar
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A79:
On Sets Whose Subsets Have Integer Mean
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A80:
Weighted Partitions and Generalized r-Lah Numbers
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Hacène Belbachir, Amine Belkhir, and Imad-Eddine Bousbaa
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A81:
The Natural Density of Some Sets of Square-free Numbers
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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
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A83:
The n-color Partition Function and Some Counting Theorems
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Subhajit Bandyopadhyay and Nayandeep Deka Baruah
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A84:
On Representations of the Riemann Zeta Function, Its Square and of the Positive Integers
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A85:
Parity Palindrome Compositions
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George E. Andrews and Greg Simay
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A86:
On Some p-adic Properties and Supercongruences of Delannoy and Schröder Numbers
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A87:
Exceptional Totient Numbers
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Breille Duncan, Joshua Harrington, and Andrew Vincent
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A88:
Will the Real Hardy--Ramanujan Formula Please Stand Up?
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A89:
Arithmetic Subsequences in a Random Ordering of an Additive Set
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Marcel K. Goh and Rosie Y. Zhao
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A90:
Geometric Patterns in The Determinant Hosoya Triangle
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Matthew Blair, Rigoberto Flórez, and Antara Mukherjee
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A91:
Fibonacci Colored Compositions and Applications
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Juan B. Gil and Jessica A. Tomasko
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A92:
Algorithms for the Multiplication Table Problem
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Richard Brent, Carl Pomerance, David Purdum, and Jonathan Webster
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A93:
Small Solutions of \(ax_1\cdots x_k + bx_{k+1}\cdots x_{2k} \equiv c \pmod{m}\) under the Lindelöf Hypothesis
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Todd Cochrane and Sanying Shi
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A94:
Sums over Primes
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A95:
Recurrence Relations for Generalized Laguerre Polynomials
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A96:
Extrema of Luroth Digits and a Zeta Function Limit Relation
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Jayadev S. Athreya and Krishna B. Athreya
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A97:
Maximum Distances in the Four-digit Kaprekar Process
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A98:
On the Equality of Dedekind Sums
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A99:
Representation Numbers of Spinor Regular Ternary Quadratic Forms
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Zafer Selcuk Aygin, Greg Doyle, Florian Münkel, Lerna Pehlivan, and Kenneth S. Williams
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A100:
Chebyshev-Fibonacci Polynomial Relations Using Generating Functions
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Robert Frontczak and Taras Goy
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A101:
High Degree b-Niven Numbers
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A102:
Values of Weighted Davenport Constants
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Rene Ardila, Christine Caples, Helen G. Grundman, Laura L. Hall-Seelig, Jill E. Jordan, Karen T. Kohl, and Thomas P. Wakefield
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A103:
Three Imprimitive Character Sums
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A104:
Multidimensional Small Divisor Functions
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A105:
Abundance of Arithmetic Progressions in Some Combinatorially Rich Sets by Elementary Means
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Pintu Debnath and Sayan Goswami
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A106:
On (Yet Another) Family of Stirling Polynomials of the Second Kind
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A107:
WZ Proofs for Lemniscate-like Constant Evaluations
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A108:
On Pillai's Problem with Lucas Numbers and Powers of 3
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Bilizimbéyé Edjeou, Amadou Tall, and Mohamed Ben Fraj Ben Maaouia
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A109:
Lucas-Lehmer Primality Tests for Certain Prime Curios
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E. L. Roettger and H. C. Williams
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A110:
Some Diophantine Problems Concerning a Pair of Rational Triangles with a Common Circumradius
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A111:
Proof of Two Conjectures of Andrica and Bagdasar
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A112:
Gibonacci Polynomial Products with Implications
Games Articles
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G1:
A Codex of N- and P-positions in Harary's 'Caterpillar Game'
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Richard M. Low, Ardak Kapbasov, Arman Kapbasov, Stephen C. Locke, and W. H. Chan
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G2:
Amalgamation Nim
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S.C. Locke and B. Handley
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G3:
On the Additive Period Length of the Sprague-Grundy Function of Certain Nim-like Games
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G4:
More about Exact Slow k-Nim
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Nikolay Chikin, Vladimir Gurvich, Konstantin Knop, Mike Paterson, and Michael Vyalyi