
Integers
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"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.
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Content
2 - CONTENTS [Seite 7]
3 - SIMPLE ARITHMETICAL CRITERIA FOR IRREDUCIBILITY OF POLYNOMIALS WITH INTEGER COEFFICIENTS [Seite 13]
4 - A SHORT PROOF OF A RESULT OF GICA AND LUCA [Seite 34]
5 - COUNTING HERON TRIANGLES WITH CONSTRAINTS [Seite 36]
6 - RAMSEY TYPE RESULTS ON THE SOLVABILITY OF CERTAIN EQUATIONS IN ZM [Seite 53]
7 - A COMBINATORIAL PROOF OF S-ADICITY FOR SEQUENCES WITH LINEAR COMPLEXITY [Seite 62]
8 - ON INTERPOLATING POWER SERIES [Seite 81]
9 - CAPTURED-REVERSIBLE MOVES AND STAR DECOMPOSITION DOMINATION IN HEX [Seite 87]
10 - ON BOUNDS FOR TWO DAVENPORT-TYPE CONSTANTS [Seite 101]
11 - ON THE DIOPHANTINE EQUATION x² - kxy + y² + lx = 0 [Seite 104]
12 - ON A SEQUENCE OF POLYNOMIALS WITH HYPOTHETICALLY INTEGER COEFFICIENTS [Seite 112]
13 - ON DIVISIBILITY PROPERTIES OF SOME DIFFERENCES OF THE CENTRAL BINOMIAL COEFFICIENTS AND CATALAN NUMBERS [Seite 141]
14 - GENERALIZED BINOMIAL EXPANSIONS AND BERNOULLI POLYNOMIALS [Seite 161]
15 - THE DISTRIBUTION OF SOLUTIONS TO xy = n (mod a) WITH AN APPLICATION TO FACTORING INTEGERS [Seite 174]
16 - DISTRIBUTION LAWS OF PAIRS OF DIVISORS [Seite 194]
17 - SHARP THRESHOLD ASYMPTOTICS FOR THE EMERGENCE OF ADDITIVE BASES [Seite 207]
18 - ON AN ANALOGUE TO THE LUCAS-LEHMER-RIESEL TEST USING ELLIPTIC CURVES [Seite 224]
19 - RESTRICTED INTEGER PARTITION FUNCTIONS [Seite 240]
20 - BRUN MEETS SELMER [Seite 249]
21 - THICK SUBSETS THAT DO NOT CONTAIN ARITHMETIC PROGRESSIONS [Seite 261]
22 - COFINITE INDUCED SUBGRAPHS OF IMPARTIAL COMBINATORIAL GAMES: AN ANALYSIS OF CIS-NIM [Seite 271]
23 - PIRATES AND TREASURE [Seite 298]
24 - TAKING THE CONVOLUTED OUT OF BERNOULLI CONVOLUTIONS: A DISCRETE APPROACH [Seite 316]
25 - SOME RESULTS ON BALANCING, COBALANCING, (a, b)-TYPE BALANCING, AND (a, b)-TYPE COBALANCING NUMBERS [Seite 328]
26 - VALUATIONS AND COMBINATORICS OF TRUNCATED EXPONENTIAL SUMS [Seite 342]
27 - STRICT SCHUR NUMBERS [Seite 358]
28 - ON q-ANALOG OF WOLSTENHOLME TYPE CONGRUENCES FOR MULTIPLE HARMONIC SUMS [Seite 370]
29 - ON THE FOURIER TRANSFORM OF THE GREATEST COMMON DIVISOR [Seite 381]
30 - WEIGHTED LONESUM MATRICES AND THEIR GENERATING FUNCTION [Seite 397]
31 - ON MULTIPLICATIVE SIDON SETS [Seite 404]
32 - SOME WEIGHTED SUMS OF PRODUCTS OF LUCAS SEQUENCES [Seite 414]
33 - ADDITIVE ENERGY AND THE FALCONER DISTANCE PROBLEM IN FINITE FIELDS [Seite 423]
34 - A COMBINATORIAL INTERPRETATION OF THE CATALAN AND BELL NUMBER DIFFERENCE TABLES [Seite 433]
35 - PISOT NUMBERS AND CHROMATIC ZEROS [Seite 452]
36 - COORDINATE SUM AND DIFFERENCE SETS OF d-DIMENSIONAL MODULAR HYPERBOLAS [Seite 459]
37 - AN INFINITE FAMILY OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF KLOOSTERMAN SUMS WITH TRACE ONE ARGUMENTS: O(2n + 1, 2r) CASE [Seite 475]
38 - THE DIOPHANTINE EQUATION Fyn + Fxn+1 = Fxm [Seite 491]
39 - A NOTE ON THE MULTIPLICATIVE STRUCTURE OF AN ADDITIVELY SHIFTED PRODUCT SET AA + 1 [Seite 508]
40 - REPRESENTATIONS OF SQUARES BY CERTAIN SEPTENARY QUADRATIC FORMS [Seite 516]
41 - CATALAN NUMBERS MODULO A PRIME POWER [Seite 534]
42 - GONI: PRIMES REPRESENTED BY BINARY QUADRATIC FORMS [Seite 538]
43 - A COMBINATORIAL PROOF OF TWO EQUIVALENT IDENTITIES BY FREE 2-MOTZKIN PATHS [Seite 556]
44 - IMPROVING THE CHEN AND CHEN RESULT FOR ODD PERFECT NUMBERS [Seite 564]
45 - FINITE SUMS THAT INVOLVE RECIPROCALS OF PRODUCTS OF GENERALIZED FIBONACCI NUMBERS [Seite 572]
46 - COMPOSITIONS CONSTRAINED BY GRAPH LAPLACIAN MINORS [Seite 583]
47 - EDGE GROWTH IN GRAPH SQUARES [Seite 605]
48 - NEW BOUNDS AND COMPUTATIONS ON PRIME-INDEXED PRIMES [Seite 625]
49 - GAP DISTRIBUTION OF FAREY FRACTIONS UNDER SOME DIVISIBILITY CONSTRAINTS [Seite 646]
50 - ONE FINITE SUMS AND INTEGRAL REPRESENTATIONS [Seite 661]
51 - FINE-WILF GRAPHS AND THE GENERALIZED FINE-WILF THEOREM [Seite 673]
52 - ON THE LEAST SIGNIFICANT 2-ADIC AND TERNARY DIGITS OF CERTAIN STIRLING NUMBERS [Seite 691]
53 - ON THE DENSITY OF HAPPY NUMBERS [Seite 701]
54 - A REMARK ON RELATIVELY PRIME SETS [Seite 726]
55 - INTERSECTING RATIONAL BEATTY SEQUENCES [Seite 740]
56 - NEW PROOFS FOR THE p, q-ANALOGUE OF CHU-VANDERMONDE'S IDENTITY [Seite 753]
57 - REMARKS ON TINY ZERO-SUM SEQUENCES [Seite 764]
58 - A NOTE ON IRREGULARITIES OF DISTRIBUTION [Seite 772]
59 - GENERALIZING DELANNOY NUMBERS VIA COUNTING WEIGHTED LATTICE PATHS [Seite 776]
60 - ON THE LEAST PRIMITIVE ROOT EXPRESSIBLE AS A SUM OF TWO SQUARES [Seite 809]
61 - STABILIZATION OF COEFFICIENTS FOR PARTITION POLYNOMIALS [Seite 816]
62 - ON SETS WITH MORE RESTRICTED SUMS THAN DIFFERENCES [Seite 831]
63 - ON AN INCOMPLETE ARGUMENT OF ERDO [Seite ON AN INCOMPLETE ARGUMENT OF ERDO]
S ON THE IRRATIONALITY OF LAMBERT SERIES - 855 [Seite 855]
64 - GENERALIZATION OF UNIVERSAL PARTITION AND BIPARTITION THEOREMS [Seite 861]
65 - SOME WEIGHTED SUMS OF POWERS OF FIBONACCI POLYNOMIALS [Seite 872]
66 - CONGRUENCES OF CONCAVE COMPOSITION FUNCTIONS [Seite 891]
67 - DISJUNCTIVE RADO NUMBERS FOR ax1 + x2 = x3 AND bx1 + x2 = x3 [Seite DISJUNCTIVE RADO NUMBERS FOR ax1 + x2 = x3 AND bx1 + x2 = x3]
- 898 [Seite 898]
68 - HOW TO WRITE A PERMUTATION AS A PRODUCT OF INVOLUTIONS (AND WHY YOU MIGHT CARE) [Seite 909]
69 - ON THE HIGHER-DIMENSIONAL GENERALIZATION OF A PROBLEM OF ROTH [Seite 929]
70 - INDEPENDENT DIVISIBILITY PAIRS ON THE SET OF INTEGERS FROM 1 TO N [Seite 936]
71 - CYCLES IN REPEATED EXPONENTIATION MODULO pn [Seite 949]
72 - COMPUTATION OF AN IMPROVED LOWER BOUND TO GIUGA'S PRIMALITY CONJECTURE [Seite 956]
73 - CONVOLUTION SUMS INVOLVING LEGENDRE-JACOBI SYMBOL AND DIVISOR FUNCTIONS [Seite 970]
74 - OPTIMAL PRIMITIVE SETS WITH RESTRICTED PRIMES [Seite 984]
75 - A ZERO-SUM THEOREM OVER Z [Seite 994]
76 - ON THE DIVISIBILITY OF an ± bn [Seite ON THE DIVISIBILITY OF an ± bn]
BY POWERS OF n - 1005 [Seite 1005]
77 - LOWER BOUNDS FOR SUMSETS OF MULTISETS IN Z2p [Seite LOWER BOUNDS FOR SUMSETS OF MULTISETS IN Z2p]
- 1011 [Seite 1011]
78 - ON SEQUENCES WITHOUT GEOMETRIC PROGRESSIONS [Seite 1028]
79 - INCLUSION-EXCLUSION POLYNOMIALS WITH LARGE COEFFICIENTS [Seite 1033]
80 - AN EXPLICIT FORMULA FOR HIGHER ORDER BERNOULLI POLYNOMIALS OF THE SECOND KIND [Seite 1036]
81 - A NOTE ON A CONJECTURE OF ERDO [Seite A NOTE ON A CONJECTURE OF ERDO]
S, GRAHAM, AND SPENCER - 1043 [Seite 1043]
82 - SQUARES AND DIFFERENCE SETS IN FINITE FIELDS [Seite 1049]
83 - A FAMILY OF FIBONACCI-LIKE CONDITIONAL SEQUENCES [Seite 1054]
84 - ON THE RESIDUE CLASSES OF p [Seite ON THE RESIDUE CLASSES OF p]
(n) MODULO t - 1068 [Seite 1068]
85 - S-DIOPHANTINE QUADRUPLES WITH TWO PRIMES CONGRUENT TO 3 MODULO 4 [Seite 1078]
86 - THE AVERAGE LARGEST PRIME FACTOR [Seite 1087]
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