INTEGERS, Volume 22 (2022)

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• A1: Two Infinite Families of Elliptic Curves with Rank Greater than One
  • Jeffrey Hatley and Jason Stack
    • Abstract
      DOI: 10.5281/zenodo.10952104
• A2: Coprime Matchings
  • Carl Pomerance
    • Abstract
      DOI: 10.5281/zenodo.10952142
• A3: Patrolling the Border of a Striking Conjecture
  • Aviezri S. Fraenkel
    • Abstract
      DOI: 10.5281/zenodo.10952184
• A4: Integer Circulant Determinants of Order 15
  • Bishnu Paudel and Chris Pinner
    • Abstract
      DOI: 10.5281/zenodo.10952236
• A5: The Diophantine Equation \(\sum_{j=1}^{k}jF_j^p=L_n^q\)
  • Souleymane Nansoko, Euloge Tchammou, and A. Togbé
    • Abstract
      DOI: 10.5281/zenodo.10952246
• A6: On Elliptic Carmichael Numbers in Arithmetic Progressions
  • Nick Egbert
    • Abstract
      DOI: 10.5281/zenodo.10952256
• A7: Inverse Problems Related to Some Weighted Zero-sum Constants for Cyclic Groups
  • Sukumar Das Adhikari, Shruti Hedge, Md Ibrahim Molla, and Subha Sarkar
    • Abstract
      DOI: 10.5281/zenodo.10952258
• A8: Divisibility and Arithmetic Properties of a Class of Sparse Polynomials
  • Karl Dilcher and Maciej Ulas
    • Abstract
      DOI: 10.5281/zenodo.10952260
• A9: Sums of Consecutive Prime Squares
  • Janyarak Tongsomporn, Saeree Wananiyakul, and Jörn Steuding
    • Abstract
      DOI: 10.5281/zenodo.10952266
• A10: Distributions of Fourier Coefficients of Cusp Forms over Arithmetic Progressions
  • Aiyue Zou, Huixue Lao, and Linli Wei
    • Abstract
      DOI: 10.5281/zenodo.10952270
• A11: A Determinant of the Artin-Hasse Exponential Coefficients
  • Matthew Schmidt
    • Abstract
      DOI: 10.5281/zenodo.10952272
• A12: An Effective Version of a Theorem of Shioda on the Ranks of Elliptic Curves Given by \(y^2=f(x)+m^2\)
  • P. G. Walsh
    • Abstract
      DOI: 10.5281/zenodo.10952278
• A13: Zero-sum-free Tuples and Hyperplane Arrangements
  • Sunil K. Chebolu and Papa A. Sissokho
    • Abstract
      DOI: 10.5281/zenodo.10952281
• A14: Additive Representations of Natural Numbers
  • Forrest J. Francis and Ethan S. Lee
    • Abstract
      DOI: 10.5281/zenodo.10952286
• A15: Minimally Intersective Polynomials with Arbitrarily Long Factorization
  • Bhawesh Mishra
    • Abstract
      DOI: 10.5281/zenodo.10952290
• A16: Fermat Numbers in Narayana's Cows Sequence
  • Kisan Bhoi and Prasanta Kumar Ray
    • Abstract
      DOI: 10.5281/zenodo.10952292
• A17: Complementary Numerical Sets
  • Matthew Guhl, Jazmine Juarez, Vadim Ponomarenko, Rebecca Rechkin, and Deepesh Singhal
    • Abstract
      DOI: 10.5281/zenodo.10952294
• A18: A Family of Unsplittable Minimal Zero-sum Sequences
  • Fang Chen
    • Abstract
      DOI: 10.5281/zenodo.10952298
• A19: Generalized Hyper-Fibonacci Numbers and Applications
  • Lyes Ait-Amrane and Djilali Behloul
    • Abstract
      DOI: 10.5281/zenodo.10952302
• A20: Partial Sums of Horadam Sequences: Sum-free Representations via Generating Functions
  • Helmut Prodinger
    • Abstract
      DOI: 10.5281/zenodo.10952308
• A21: The Three Gap Theorem and Periodic Functions
  • A. Suki Dasher, A. Hermida, and Tian An Wong
    • Abstract
      DOI: 10.5281/zenodo.10952312
• A22: The Continued Fraction Map Composed with Fractional Linear Maps
  • Fritz Schweiger
    • Abstract
      DOI: 10.5281/zenodo.10963827
• A23: Relations between Derangement and Factorial Numbers
  • Adem Şahin
    • Abstract
      DOI: 10.5281/zenodo.10963831
• A24: Equivalence Classes of Skew Dyck Paths Modulo Some Patterns
  • Jean-Luc Baril, José Luis Ramírez, and Lina Maria Simbaqueba
    • Abstract
      DOI: 10.5281/zenodo.10963833
• A25: Trace and Discriminant Criteria for a Matrix to Be a Sum of Sixth and Eighth Powers of Matrices
  • Rakesh Barai and Anuradha S. Garge
    • Abstract
      DOI: 10.5281/zenodo.10963837
• A26: An Inequality for the Distribution of Numbers Free of Small Prime Factors
  • Kai (Steve) Fan
    • Abstract
      DOI: 10.5281/zenodo.10963840
• A27: Finding Almost Squares VII
  • Tsz Ho Chan
    • Abstract
      DOI: 10.5281/zenodo.10963844
• A28: A Note on a Generalization of Two Well-Known Combinatorial Identities via a Hypergeometric Series Approach
  • Arjun K. Rathie, Insuk Kim, and Richard B. Paris
    • Abstract
      DOI: 10.5281/zenodo.10963847
• A29: On the Diophantine Equation \(7^{x}+32^{y}=z^{2}\) and its Generalization
  • Padma Bhushan Borah and Mridul Dutta
    • Abstract
      DOI: 10.5281/zenodo.10963852
• A30: An Expression for the Legendre Symbol from a Product-Sum Formula
  • B. Sury
    • Abstract
      DOI: 10.5281/zenodo.10963854
• A31: On a Family of Cubic Thue Equations Involving Fibonacci and Lucas Numbers
  • Tobias Hilgart, Ingrid Vukusic, and Volker Ziegler
    • Abstract
      DOI: 10.5281/zenodo.10963858
• A32: Sequences in Partitions
  • George E. Andrews, Sreerupa Bhattacharjee, and Manosij G. Dastidar
    • Abstract
      DOI: 10.5281/zenodo.10963936
• A33: On Some Generalizations to Floor Function Identities of Ramanujan
  • Sai Teja Somu and Andrzej Kukla
    • Abstract
      DOI: 10.5281/zenodo.10963942
• A34: Two Complementary Relations for the Rogers-Ramanujan Continued Fraction
  • Sumit Kumar Jha
    • Abstract
      DOI: 10.5281/zenodo.10963950
• A35: A Bijection Between Symmetric Valleys in Dyck Paths and Even Degree Interval Vertices in Ordered Trees
  • Farzan Byramji
    • Abstract
      DOI: 10.5281/zenodo.10963956
• A36: The \(\{1,s\}\)-Weighted Davenport Constant in \(C_{n}^{k}\)
  • Fabio Enrique Brochero Martínez and Sávio Ribas
    • Abstract
      DOI: 10.5281/zenodo.10963965
• A37: Additive Bases of Finite Abelian Groups of Rank 2
  • Weidong Gao, Yuanlin Li, Yongke Qu, and Qinghong Wang
    • Abstract
      DOI: 10.5281/zenodo.10963976
• A38: On Primary Carmichael Numbers
  • Bernd C. Kellner
    • Abstract
      DOI: 10.5281/zenodo.10963985
• A39: Power of a 3 x 3 Matrix, Subgroups and Tiling
  • Juri Kirillov
    • Abstract
      DOI: 10.5281/zenodo.10963988
• A40: Two-Dimensional, Three-Dimensional and n-Dimensional Recurrence Relations of Jacobsthal
  • Milena Carolina dos Santos Mangueira, Renata Passos Machado Vieira, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino, and Renata Teófilo de Sousa
    • Abstract
      DOI: 10.5281/zenodo.10963994
• A41: Prime Floor and Prime Ceiling Functions
  • Abhimanyu Kumar
    • Abstract
      DOI: 10.5281/zenodo.10964004
• A42: A Matrix Related to Stern Polynomials and the Prouhet-Thue-Morse Sequence
  • George Beck and Karl Dilcher
    • Abstract
      DOI: 10.5281/zenodo.10964015
• A43: Multiplicative Functions k-Additive on Generalized Pentagonal Numbers
  • Elchin Hasanalizade
    • Abstract
      DOI: 10.5281/zenodo.10983975
• A44: A Proof of Euler's Theorem via Quandles
  • António Lages and Pedro Lopes
    • Abstract
      DOI: 10.5281/zenodo.10983986
• A45: Note on Sets without Geometric Progressions
  • Xue-Qin Cao, Jin-Hui Fang, and Nathan McNew
    • Abstract
      DOI: 10.5281/zenodo.10987309
• A46: Solution to a Problem Due to Chu and Kiliç
  • John Maxwell Campbell
    • Abstract
    • Associated Computer Programs
      Mathematica Notebook (zip file)
      
      DOI: 10.5281/zenodo.10987326
• A47: Subgraphs of Coprime Graphs on Sets of Consecutive Integers
  • Ethan Berkove and Michael Brilleslyper
    • Abstract
      DOI: 10.5281/zenodo.10987344
• A48: On the Generalized Leonardo Numbers
  • Kantaphon Kuhapatanakul and Juthamas Chobsorn
    • Abstract
      DOI: 10.5281/zenodo.10987378
• A49: Counting the Parts Divisible by k in All the Partitions of n Whose Parts Have Multiplicity Less than k
  • Daniel Herden, Mark R. Sepanski, Jonathan Stanfill, Cordell C. Hammon, Joel Henningsen, Henry Ickes, Jorge Marchena Menendez, Taylor Poe, Indalecio Ruiz, and Edward L. Smith
    • Abstract
      DOI: 10.5281/zenodo.10987396
• A50: A Generalization of an Inequality by Graham
  • Curtis Cooper
    • Abstract
      DOI: 10.5281/zenodo.10987417
• A51: Sum and Mod Sum Graphs of Arithmetic Sets
  • Meeri-Liisa Beste, Jan-Hendrik de Wiljes, and Martin Kreh
    • Abstract
      DOI: 10.5281/zenodo.10987430
• A52: Arithmetic Convergence of Double-Iterated Polynomials
  • Rin Gotou
    • Abstract
      DOI: 10.5281/zenodo.10987438
• A53: A Generalization of the Hardy-Littlewood Conjecture
  • Emre Alkan
    • Abstract
      DOI: 10.5281/zenodo.10987450
• A54: Polygonal Balancing Numbers I
  • Jeremiah Bartz, Bruce Dearden, and Joel Iiams
    • Abstract
      DOI: 10.5281/zenodo.10987461
• A55: Primary Carmichael Numbers
  • Samuel S. Wagstaff, Jr.
    • Abstract
      DOI: 10.5281/zenodo.10987475
• A56: Hypergeometric Bernoulli Polynomials and r-Associated Stirling Numbers of the Second Kind
  • Paolo Emilio Ricci and Pierpaolo Natalini
    • Abstract
      DOI: 10.5281/zenodo.10991766
• A57: Embedding Theory of Lattices and Its Application to 2-Integrable Lattices
  • Qianqian Yang and Kiyoto Yoshino
    • Abstract
      DOI: 10.5281/zenodo.10991776
• A58: On the Index of Odd Perfect Numbers
  • Luis H. Gallardo
    • Abstract
      DOI: 10.5281/zenodo.10991778
• A59: Primes in Floor Function Sets
  • Randell Heyman
    • Abstract
    • Errata
      Errata
      
      DOI: 10.5281/zenodo.10991782
• A60: On Hyper k-Pell, Hyper k-Pell-Lucas and Hyper Modified k-Pell Sequences
  • Paula Catarino, Francisco R. V. Alves, and Helena Campos
    • Abstract
      DOI: 10.5281/zenodo.10991790
• A61: p-Adic Order of Positive Integers via Binomial Coefficients
  • Dario T. de Castro
    • Abstract
      DOI: 10.5281/zenodo.10991800
• A62: Schur's Theorem in Integer Lattices
  • Vishal Balaji, Andrew Lott, and Alex Rice
    • Abstract
      DOI: 10.5281/zenodo.10991804
• A63: Combinatorial Formulas for Arithmetic Density
  • Robert Schneider and Andrew V. Sills
    • Abstract
      DOI: 10.5281/zenodo.10991814
• A64: k-Fibonacci Numbers and Möbius Functions
  • Emil Daniel Schwab and Gabriela Schwab
    • Abstract
      DOI: 10.5281/zenodo.10991823
• A65: Alternating N-Expansions
  • Karma Dajani and Niels Langeveld
    • Abstract
      DOI: 10.5281/zenodo.10991842
• A66: Some Remarks on Harmonic Type Matrices
  • Haydar Göral
    • Abstract
      DOI: 10.5281/zenodo.10991851
• A67: Permanents of 3 x 3 Invertible Matrices Modulo n
  • Ayush Bohra and A. Satyanarayana Reddy
    • Abstract
      DOI: 10.5281/zenodo.10991856
• A68: On the 2-Adic Valuation of Generalized Fibonacci Sequences
  • Paul Thomas Young
    • Abstract
      DOI: 10.5281/zenodo.10991870
• A69: Irreducibility of Generalized Fibonacci Polynomials
  • Rigoberto Flórez and J. C. Saunders
    • Abstract
      DOI: 10.5281/zenodo.10991876
• A70: Arithmetic Properties of the Ternary Quadratic Form \(3x^2+6y^2+14z^2+4yz+2zx+2xy\)
  • Florian Münkel, Lerna Pehlivan, and Kenneth S. Williams
    • Abstract
      DOI: 10.5281/zenodo.10991892
• A71: Prime Factors of \(\Phi_3(x)\) of the Same Form
  • Cody S. Hansen and Pace P. Nielsen
    • Abstract
      DOI: 10.5281/zenodo.10991904
• A72: A q-Analogue of Granville's Congruence
  • Laid Elkhiri, Neşe Ömür, and Sibel Koparal
    • Abstract
      DOI: 10.5281/zenodo.10991912
• A73: Full k-Complete Partitions
  • Augustine O. Munagi and Ntendeni A. Takalani
    • Abstract
      DOI: 10.5281/zenodo.10995932
• A74: Average Behavior of the Fourier Coefficients of the Symmetric Square L-Function over Some Sequence of Integers
  • Anubhav Sharma and Ayyadurai Sankaranarayanan
    • Abstract
      DOI: 10.5281/zenodo.10995938
• A75: The Repetends of Reduced Fractions a/b^k Approach Full Complexity with an Increasing k
  • Josefina López and Peter Stoll
    • Abstract
      DOI: 10.5281/zenodo.10995942
• A76: Some Primality Conditions for N=2pⁿ-1
  • E. L. Roettger and H. C. Williams
    • Abstract
      DOI: 10.5281/zenodo.10995948
• A77: On the Computation of Fundamental Periods of v-Palindromic Numbers
  • Daniel Tsai
    • Abstract
      DOI: 10.5281/zenodo.10995952
• A78: Faulhaber's Formula, Odd Bernoulli Numbers, and the Method of Partial Sums
  • Ryan Zielinski
    • Abstract
      DOI: 10.5281/zenodo.10995964
• A79: Unfair Distributions Counted by the Generalized Stirling Numbers
  • Beáta Bényi, Sithembele Nkonkobe, and Mark Shattuck
    • Abstract
      DOI: 10.5281/zenodo.10995968
• A80: Coefficients of Unitary Cyclotomic Polynomials of Order Three
  • Gennady Bachman
    • Abstract
      DOI: 10.5281/zenodo.10995976
• A81: Sums of Products of Binomial Coefficients Mod 2 and Run Length Transforms of Sequences
  • Chai Wah Wu
    • Abstract
      DOI: 10.5281/zenodo.10995985
• A82: New Results on the p-Adic Valuation of Stirling Numbers
  • Arnold Adelberg and Tamás Lengyel
    • Abstract
      DOI: 10.5281/zenodo.10995993
• A83: Coprime Permutations
  • Carl Pomerance
    • Abstract
      DOI: 10.5281/zenodo.10995995
• A84: The Order of the Fundamental Solution of \(x^2-Dy^2 =1\) in \(\mathbb{Z}[\sqrt{D}]/\langle D \rangle\)
  • Stephen Choi and Daniel Tarnu
    • Abstract
      DOI: 10.5281/zenodo.10996005
• A85: Extension of an Inequality for Fibonacci Numbers
  • Horst Alzer and Man Kam Kwong
    • Abstract
      DOI: 10.5281/zenodo.10997241
• A86: A Note on the Wilson Quotient
  • Takashi Agoh
    • Abstract
      DOI: 10.5281/zenodo.10997247
• A87: Multiplicative Functions Which Are Additive on Sums of Two Nonzero Squares
  • Poo-Sung Park
    • Abstract
      DOI: 10.5281/zenodo.10997249
• A88: On Denseness of Certain Direction and Generalized Direction Sets
  • Deepa Antony, Rupam Barman, and Jaitra Chattopadhyay
    • Abstract
      DOI: 10.5281/zenodo.10997253
• A89: A Class of Graphs Based on a Set of Moduli
  • A. David Christopher
    • Abstract
      DOI: 10.5281/zenodo.10997273
• A90: On the Two-Color Rado Number for \(\sum_{i=1}^{m-2} x_i+ax_{m-1}-x_m=c\)
  • Srashti Dwivedi and Amitabha Tripathi
    • Abstract
      DOI: 10.5281/zenodo.10997280
• A91: Loop Decompositions of Random Walks and Nontrivial Identities of Bernoulli and Euler Polynomials
  • Lin Jiu, Italo Simonelli, and Heng Yue
    • Abstract
      DOI: 10.5281/zenodo.10997290
• A92: Hypergraph Ramsey Numbers Involving Trees, Stars, and Complete Hypergraphs
  • Mark Budden and Justin Clifton
    • Abstract
      DOI: 10.5281/zenodo.10997300
• A93: Extremal Sequences for a Weighted Zero-Sum Constant
  • Santanu Mondal, Krishnendu Paul, and Shameek Paul
    • Abstract
      DOI: 10.5281/zenodo.10997305
• A94: Partial Dyck paths with Air Pockets
  • Helmut Prodinger
    • Abstract
      DOI: 10.5281/zenodo.10997311
• A95: Some Summation and Transformation Formulas from Inversion Techniques
  • Chuanan Wei, Yi Wei, and Chun Li
    • Abstract
      DOI: 10.5281/zenodo.10997318
• A96: Quotients of Palindromic and Antipalindromic Numbers
  • James Haoyu Bai, Joseph Meleshko, Samin Riasat, and Jeffrey Shallit
    • Abstract
      DOI: 10.5281/zenodo.10997324
• A97: Generalized Sum-Free Sets and Cycle Saturated Regular Graphs
  • David Davini and Craig Timmons
    • Abstract
      DOI: 10.5281/zenodo.10997330
• A98: Linear Combinations of Dirichlet Series Associated with the Thue-Morse Sequence
  • László Tóth
    • Abstract
      DOI: 10.5281/zenodo.10997336
• A99: On a Conjecture of Deaconescu
  • Elchin Hasanalizade
    • Abstract
      DOI: 10.5281/zenodo.10997342
• A100: On the Diophantine Equations \(F_n=P_m \pm P_{\ell}\) and \(P_n= F_m \pm F_{\ell}\) Involving Fibonacci and Pell Numbers
  • Salah Eddine Rihane
    • Abstract
      DOI: 10.5281/zenodo.10997347
• A101: Lattices of Minimal Index in \(\mathbb{Z}^n\) Having an Orthogonal Basis Containing a Given Vector
  • Chris Pinner and Chris Smyth
    • Abstract
      DOI: 10.5281/zenodo.10999212
• A102: Higher Degree Erdős-Ginzburg-Ziv Constants
  • Yair Caro and John R. Schmitt
    • Abstract
      DOI: 10.5281/zenodo.10999216
• A103: Weighted Free Lattice Paths and Legendre Polynomials
  • Teresa X.S. Li and Alina F.Y. Zhao
    • Abstract
      DOI: 10.5281/zenodo.10999225
• A104: A Tiling Interpretation of a Generalized Zeckendorf's Theorem
  • Arthur T. Benjamin and John Lentfer
    • Abstract
      DOI: 10.5281/zenodo.10999231
• A105: On the Brousseau Sums \(\sum_{i=1}^n i^p F_i\)
  • Gregory Dresden
    • Abstract
      DOI: 10.5281/zenodo.10999238
• A106: Multiplicative Inequalities for Primes and the Prime Counting Function
  • Joel E. Cohen
    • Abstract
      DOI: 10.5281/zenodo.10999241
• A107: On the x-Coordinates of Pell Equations Which Are Narayana Numbers
  • Kisan Bhoi and Prasanta Kumar Ray
    • Abstract
      DOI: 10.5281/zenodo.10999245
• A108: A Parametrized Set of Explicit Elements of Ш\((E/\mathbb{Q})[3]\)
  • Steven R. Groen and Jaap Top
    • Abstract
      DOI: 10.5281/zenodo.10999247
• A109: Congruences Related to the Wilson Quotient
  • Takashi Agoh
    • Abstract
      DOI: 10.5281/zenodo.10999250
• A110: Fibonacci-Catalan Series
  • Kunle Adegoke, Robert Frontczak, and Taras Goy
    • Abstract
      DOI: 10.5281/zenodo.10999260
• A111: Formations and Generalized Davenport-Schinzel Sequences
  • Jesse Geneson, Peter Tian, and Katherine Tung
    • Abstract
      DOI: 10.5281/zenodo.10999272
• A112: Direct and Inverse Problems for Subset Sums with Certain Restrictions
  • Himanshu Kumar Dwivedi and Raj Kumar Mistri
    • Abstract
      DOI: 10.5281/zenodo.10999274
• A113: Sums of ω(n) and Ω(n) over the k-Free Parts and k-Full Parts of Some Particular Sequences
  • Rafael Jakimczuk and Matilde Lalín
    • Abstract
      DOI: 10.5281/zenodo.10999279
• A114: A Generalization of Quasi-Shuffle Algebras and an Application to Multiple Zeta Values
  • Adam Keilthy
    • Abstract
      DOI: 10.5281/zenodo.10999355
• A115: Ideal Solutions of the Tarry-Escott Problem of Degree Seven
  • Ajai Choudhry
    • Abstract
      DOI: 10.5281/zenodo.10999357

• G1: Diffusion and Polyominoes
  • Todd Mullen, Richard J. Nowakowski, and Danielle Cox
    • Abstract
      DOI: 10.5281/zenodo.10999623
• G2: Pyramid Nim
  • Stephen J. Curran, Daniel Gray, Stephen C. Locke, and Richard M. Low
    • Abstract
      DOI: 10.5281/zenodo.10999630
• G3: On the Combinatorial Value of Hex Positions
  • Peter Selinger
    • Abstract
      DOI: 10.5281/zenodo.10999636
• G4: The Polynomial Profile of Distance Games on Paths and Cycles
  • Svenja Huntemann and Lexi Nash
    • Abstract
      DOI: 10.5281/zenodo.10999641
• G5: Transfinite Game Values in Infinite Draughts
  • Joel David Hamkins and Davide Leonessi
    • Abstract
      DOI: 10.5281/zenodo.10999646
• G6: Invertible Elements of the Dicot Misère Universe
  • Michael Fisher, Richard J. Nowakowski, and Carlos Pereira dos Santos
    • Abstract
      DOI: 10.5281/zenodo.10999648