Integers

Annual Volume 2013

Bruce Landman

• Publisher: De Gruyter
• Year: 2014
• eBook ISBN: 9783110369328
• Edition: 1
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

"Integers" is a refereed online journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. Integers also houses a combinatorial games section.

This work presents all papers of the 2013 volume in book form.

Table of contents

• Title Page
• Copyright Page
• PREFACE TO VOLUME 13 OF INTEGERS
• Table of Contents
• SIMPLE ARITHMETICAL CRITERIA FOR IRREDUCIBILITY OF POLYNOMIALS WITH INTEGER COEFFICIENTS
• A SHORT PROOF OF A RESULT OF GICA AND LUCA
• COUNTING HERON TRIANGLES WITH CONSTRAINTS
• RAMSEY TYPE RESULTS ON THE SOLVABILITY OF CERTAIN EQUATION IN ℤM
• A COMBINATORIAL PROOF OF S-ADICITY FOR SEQUENCES WITH LINEAR COMPLEXITY
• ON INTERPOLATING POWER SERIES
• CAPTURED-REVERSIBLE MOVES AND STAR DECOMPOSITION DOMINATION IN HEX
• ON BOUNDS FOR TWO DAVENPORT-TYPE CONSTANTS
• ON THE DIOPHANTINE EQUATION X2 - KXY + Y2 + LX = 0
• ON A SEQUENCE OF POLYNOMIALS WITH HYPOTHETICALLY INTEGER COEFFICIENTS
• ON DIVISIBILITY PROPERTIES OF SOME DIFFERENCES OF THE CENTRAL BINOMIAL COEFFICIENTS AND CATALAN NUMBERS
• GENERALIZED BINOMIAL EXPANSIONS AND BERNOULLI POLYNOMIALS
• THE DISTRIBUTION OF SOLUTIONS TO XY = N (MOD A) WITH AN APPLICATION TO FACTORING INTEGERS
• DISTRIBUTION LAWS OF PAIRS OF DIVISORS
• SHARP THRESHOLD ASYMPTOTICS FOR THE EMERGENCE OF ADDITIVE BASES
• ON AN ANALOGUE TO THE LUCAS-LEHMER-RIESEL TEST USING ELLIPTIC CURVES
• RESTRICTED INTEGER PARTITION FUNCTIONS
• BRUN MEETS SELMER
• THICK SUBSETS THAT DO NOT CONTAIN ARITHMETIC PROGRESSIONS
• COFINITE INDUCED SUBGRAPHS OF IMPARTIAL COMBINATORIAL GAMES: AN ANALYSIS OF CIS-NIM
• PIRATES AND TREASURE
• TAKING THE CONVOLUTED OUT OF BERNOULLI CONVOLUTIONS: A DISCRETE APPROACH
• SOME RESULTS ON BALANCING, COBALANCING, (a, b)-TYPE BALANCING, AND (a, b)-TYPE COBALANCING NUMBERS
• VALUATIONS AND COMBINATORICS OF TRUNCATED EXPONENTIAL SUMS
• STRICT SCHUR NUMBERS
• ON q-ANALOG OF WOLSTENHOLME TYPE CONGRUENCES FOR MULTIPLE HARMONIC SUMS
• ON THE FOURIER TRANSFORM OF THE GREATEST COMMON DIVISOR
• WEIGHTED LONESUM MATRICES AND THEIR GENERATING FUNCTION
• ON MULTIPLICATIVE SIDON SETS
• SOME WEIGHTED SUMS OF PRODUCTS OF LUCAS SEQUENCES
• ADDITIVE ENERGY AND THE FALCONER DISTANCE PROBLEM IN FINITE FIELDS
• A COMBINATORIAL INTERPRETATION OF THE CATALAN AND BELL NUMBER DIFFERENCE TABLES
• PISOT NUMBERS AND CHROMATIC ZEROS
• COORDINATE SUM AND DIFFERENCE SETS OF d-DIMENSIONAL MODULAR HYPERBOLAS
• AN INFINITE FAMILY OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF KLOOSTERMAN SUMSWITH TRACE ONE ARGUMENTS: O(2N + 1, 2R) CASE
• THE DIOPHANTINE EQUATION
• A NOTE ON THE MULTIPLICATIVE STRUCTURE OF AN ADDITIVELY SHIFTED PRODUCT SET AA + 1
• REPRESENTATIONS OF SQUARES BY CERTAIN SEPTENARY QUADRATIC FORMS
• CATALAN NUMBERS MODULO A PRIME POWER
• GONI: PRIMES REPRESENTED BY BINARY QUADRATIC FORMS
• A COMBINATORIAL PROOF OF TWO EQUIVALENT IDENTITIES BY FREE 2-MOTZKIN PATHS
• IMPROVING THE CHEN AND CHEN RESULT FOR ODD PERFECT NUMBERS
• FINITE SUMS THAT INVOLVE RECIPROCALS OF PRODUCTS OF GENERALIZED FIBONACCI NUMBERS
• COMPOSITIONS CONSTRAINED BY GRAPH LAPLACIAN MINORS
• EDGE GROWTH IN GRAPH SQUARES
• NEW BOUNDS AND COMPUTATIONS ON PRIME-INDEXED PRIMES
• GAP DISTRIBUTION OF FAREY FRACTIONS UNDER SOME DIVISIBILITY CONSTRAINTS
• ON FINITE SUMS AND INTEGRAL REPRESENTATIONS
• FINE-WILF GRAPHS AND THE GENERALIZED FINE-WILF THEOREM
• ON THE LEAST SIGNIFICANT 2-ADIC AND TERNARY DIGITS OF CERTAIN STIRLING NUMBERS
• ON THE DENSITY OF HAPPY NUMBERS
• A REMARK ON RELATIVELY PRIME SETS
• INTERSECTING RATIONAL BEATTY SEQUENCES
• NEW PROOFS FOR THE P, Q-ANALOGUE OF CHU-VANDERMONDE’S IDENTITY
• REMARKS ON TINY ZERO-SUM SEQUENCES
• A NOTE ON IRREGULARITIES OF DISTRIBUTION
• GENERALIZING DELANNOY NUMBERS VIA COUNTING WEIGHTED LATTICE PATHS
• ON THE LEAST PRIMITIVE ROOT EXPRESSIBLE AS A SUM OF TWO SQUARES
• STABILIZATION OF COEFFICIENTS FOR PARTITION POLYNOMIALS
• ON SETS WITH MORE RESTRICTED SUMS THAN DIFFERENCES
• ON AN INCOMPLETE ARGUMENT OF ERDŐS ON THE IRRATIONALITY OF LAMBERT SERIES
• GENERALIZATION OF UNIVERSAL PARTITION AND BIPARTITION THEOREMS
• SOME WEIGHTED SUMS OF POWERS OF FIBONACCI POLYNOMIALS
• CONGRUENCES OF CONCAVE COMPOSITION FUNCTIONS
• DISJUNCTIVE RADO NUMBERS FOR ax1 + x2 = x3 AND bx1 + x2 = x3
• HOW TO WRITE A PERMUTATION AS A PRODUCT OF INVOLUTIONS (AND WHY YOU MIGHT CARE)
• ON THE HIGHER-DIMENSIONAL GENERALIZATION OF A PROBLEM OF ROTH
• INDEPENDENT DIVISIBILITY PAIRS ON THE SET OF INTEGERS FROM 1 TO N
• CYCLES IN REPEATED EXPONENTIATION MODULO pn
• COMPUTATION OF AN IMPROVED LOWER BOUND TO GIUGA’S PRIMALITY CONJECTURE
• CONVOLUTION SUMS INVOLVING LEGENDRE-JACOBI SYMBOL AND DIVISOR FUNCTIONS
• OPTIMAL PRIMITIVE SETS WITH RESTRICTED PRIMES
• A ZERO-SUM THEOREM OVER ℤ
• ON THE DIVISIBILITY OF an ± bn BY POWERS OF n
• LOWER BOUNDS FOR SUMSETS OF MULTISETS IN
• ON SEQUENCES WITHOUT GEOMETRIC PROGRESSIONS
• INCLUSION-EXCLUSION POLYNOMIALS WITH LARGE COEFFICIENTS
• AN EXPLICIT FORMULA FOR HIGHER ORDER BERNOULLI POLYNOMIALS OF THE SECOND KIND
• A NOTE ON A CONJECTURE OF ERDŐS, GRAHAM, AND SPENCER
• SQUARES AND DIFFERENCE SETS IN FINITE FIELDS
• A FAMILY OF FIBONACCI-LIKE CONDITIONAL SEQUENCES
• ON THE RESIDUE CLASSES OF π(n) MODULO t
• S-DIOPHANTINE QUADRUPLES WITH TWO PRIMES CONGRUENT TO 3 MODULO 4
• THE AVERAGE LARGEST PRIME FACTOR