Book:Joe Roberts/Lure of the Integers
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Joe Roberts: Lure of the Integers
Published $\text {1992}$, MAA Spectrum
- ISBN 978-0883855027
Contents
- Preface
- Integers 2, 3
- 1 Equidecomposability
- 2 Cubing Cubes
- 3 Sets Congruent to a Proper Part
- 4 Random Walks
- Integer 3
- 1 Sums
- 2 Beatty's Theorem
- 3 Iterates
- 4 $\map \sigma {p^4}$
- 5 Chaos -- An Ex-"Property" of $3$"
- 6 Repeating Blocks
- 7 Sectioning a Circle
- 8 $k$-transposable Integers
- 9 Kuratowski's Theorem
- Integers 3, 4
- 1 Lattice Points in Tetrahedra
- 2 A Problem of Mnich
- 3 Polynomials Sums of Squares
- Integer 4
- 1 Davenport-Baker Theorem
- 2 Arithmetic Progressions in the Fibonacci Sequence
- 3 Factorials
- 4 The Next to Last Case of a Factorial Diophantine Equation
- 5 Hall's Theorem
- 6 Residue Classes
- 7 Diophantine Representation
- 8 Lattice Cornered Polygons
- 9 von Neumann Algebras
- 10 A Few Diophantine Equations
- 11 Four Fifth Powers
- 12 Stufe of a Real Quadratic Field
- Integers 4, 5
- 1 A Problem of Znám
- 2 An Awful Problem
- Integer 5
- 1 Euler Polynomials
- 2 Primes a Sum and a Difference of Primes
- 3 Figurate Numbers
- 4 Consecutive Primitive Roots
- 5 Five Moduli
- 6 A Conjecture Based on Goldbach's Conjecture
- 7 A Square the Sum of Three Squares
- 8 Primes as Range of a Polynomial
- 9 A Recursive Sequence
- 10 Numbers of the Form $n! + k$
- 11 Duffinian Numbers
- 12 Digital Roots
- 13 The Banach-Tarski Paradox
- 14 Euclidean Algorithm
- 15 Sieve Approaches to Twin Primes
- 16 An Extremal Property of $5$
- 17 Volumes of $n$-Dimensional Spheres
- 18 Regular Polyhedra
- Integer 6
- 1 Sum of Distinct Primes
- 2 Values of $\phi$
- 3 Divisors of $a^n - b^n$
- 4 Square Permutations
- 5 Shrinking Labelled Squares
- 6 Irreducible Polynomials
- 7 Bilinear Transformations
- 8 Polyhedra
- 9 Perfect Numbers
- 10 Mod $N$ Weak Uniform Distribution
- 11 Sophie Germain's Theorem
- 12 A Curious Sequence
- Integer 7
- 1 Incomparable Rectangles
- 2 Minimal Numbers
- 3 A Square
- 4 Iterates
- 5 Influence of Computing
- 6 Fibonacci Numbers of the Form $k^2 + 1$
- 7 A Conjecture of Ramanujan
- Integer 8
- 1 Square Identities
- 2 Parallelizability of the Spheres
- 3 Regular Lattice $n$-Simplices
- 4 A Multiplicative Function
- 5 Fibonacci Cubes
- Integer 9
- 1 Waring for Cubes
- 2 Sums of Distinct Odd Primes
- 3 An Identity
- 4 Public Key Cryptosystems
- 5 Partitions of a Set
- Integer 10
- 1 $1$, $10$ and Primes
- 2 Number of Relations
- 3 A Parlor Problem
- 4 Quasi-normal Sets of Integers
- 5 An Exponential Diophantine Equation
- Integer 11
- Sum of Distinct Primes
- Integer 12
- 1 Prime Factors of Fibonacci Numbers
- 2 Sums of Squares
- 3 Values of $\map \sigma n$ and $\map \tau n$
- 4 On the Prime Factorization of Binomial Coefficients
- Integer 13
- 1 A conjecture
- 2 Simultaneous Quadratic Equations
- 3 A Peculiar Property of $13$
- 4 Three Thirteens
- 5 The "Thirteen Spheres Controversy"
- Integer 14
- A Kuratowski Result
- Integers 15, 54, 88
- 1 Universal and Almost Universal Forms
- 2 Totitives
- 3 Waring for Fourth Powers
- Integer 16
- Integer 17
- 1 Sums of Relatively Prime Numbers
- 2 A Ramanujan Type Congruence
- 3 Consecutive Integers
- 4 The Equation $x^3 - y^2 = -17$
- 5 A Steinhaus Problem
- Integer 18
- 1 Meeting Circles
- 2 More Totitives
- 3 Sums of Mixed Powers
- Integer 19
- Waring's Problem
- Integers 20, 21
- A Matter of Purity
- Integer 21
- Squared Squares
- Integer 22
- A Special Congruence
- Integer 23
- 1 LCM of Binomial Coefficients
- 2 Pseudoprimes
- 3 Filling Boxes
- 4 Hilbert's List
- 5 Birthday Problems
- 6 The $\tau$ Function
- Integer 24
- 1 Sum of Consecutive Squares a Square
- 2 A Property of $24$
- 3 Fibonacci Periodicities
- 4 Characters
- 5 Divisors of $24$
- 6 $\map \sigma {24 n - 1}$
- 7 Self-dual Lattices in $R^n$
- 8 Some Formulae Containing $24$
- 9 A Fermat-like Equation
- Integer 25
- A Mystery
- Integer 27
- 1 Powers as Sums of Digits
- 2 Langford Sequence
- Integer 28
- A Special Perfect Number
- Integer 29
- Consecutive Integers
- Integer 30
- 1 Property of $30$
- 2 A Spurious Property
- Integer 32
- A Conjecture of Carmichael
- Integer 33
- Complete Sequences
- Integer 36
- Sums of Digits
- Integer 38
- Sums of Composites
- Integer 47
- Cutting a Cube into Cubes
- Integer 52
- A Linear Recurrence
- Integer 53
- $3$-Solubility
- Integer 67
- An Inequality on $\map \pi x$
- Integer 70
- A Curious Property
- Integer 77
- 1 Unit Fractions
- 2 Sums of Squares
- Integer 84
- Automorphisms of a Curve
- Integer 86
- A School Girl
- Integer 87
- Prime Proof
- Integer 88
- Quadratic Forms
- Integer 90
- Bi-unitary Perfect Numbers
- Integer 96
- Prime Subsequence of Primes
- Integer 100
- 1 Fibonacci Mod $100$
- 2 $100$ Digits of pi
- 3 Recursive Sets
- Integer 105
- 1 Cyclotomic Polynomials
- 2 A Question of Erdős
- 3 A Decimal Digit Problem
- 4 An Assertion of Cseh
- Integer 113
- Functions of Prime Numbers
- Integer 117
- A Diophantine Equation
- Integer 128
- Sum of Unequal Squares
- Integer 143
- Clockhands
- Integer 144
- Fibonacci Square
- Integer 163
- 1 Approximate Integers
- 2 Unique Factorization Domains
- 3 Quadratic Prime Giving Polynomials
- Integer 239
- 1 Sums of Cubes
- Integer 283
- Triplets for Primes
- Integer 495
- Kaprekar Constants
- Integer 561
- Carmichael Numbers
- Integer 563
- Wilson Remainders
- Integer 645
- Sum of Consecutive Integers
- Integer 654
- Gaps in Primes
- Integer 691
- A Divisibility Property
- Integers 714 and 715
- $714$ and $715$
- Integer 720
- Factorials
- Integer 1093
- Fermat's Conjecture
- Integer 1621
- $7$, $991$, $1141$, $1621$
- Integer 1729
- Hardy's Taxi
- Integer 1794
- The Binomial Coefficient $\binom {k^2} k$
- Integer 1848
- Numeri Idonei
- Integer 2719
- $\mathrm {MR} \ 56 \ \# \ 15557$
- Integer 3304
- Smith Numbers
- Integer 4181
- Converse Numbers
- Integer 17163
- Sums of Squares of Primes
- Integer 20161
- Abundant Numbers
- Integer 63001
- Ramanujan's $\tau$ Function
- Integer 720720
- A Divisibility Problem
- Integer 99925853
- Integer 906180359
- Integer 10513222720
- A Method of Factoring
- Integer 608981813029
- A Chebyshev Observation
- Integer 2935363331541925531
- Two Sequences of Composite Integers
- Integer 1123595505617977522809
- A Multiple of $99$
- Integer 357686312646216567629137
- Truncatable Primes
- Word/Phrase Index
- Integer Index