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Unsolved Problems in Number Theory

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ISBN-10: 0387208607

ISBN-13: 9780387208602

Edition: 3rd 2004 (Revised)

Authors: Richard K. Guy

List price: $99.99
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Description:

Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied. This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity. For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway's RATS and palindromes. The author has also included a useful new feature at the end of several of the sections: lists of references to OEIS, Neil Sloane's…    
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Book details

List price: $99.99
Edition: 3rd
Copyright year: 2004
Publisher: Springer New York
Publication date: 7/13/2004
Binding: Hardcover
Pages: 438
Size: 6.10" wide x 9.25" long x 0.50" tall
Weight: 1.738

Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
Glossary of Symbols
Prime Numbers
Prime values of quadratic functions
Primes connected with factorials
Mersenne primes
Repunits
Fermat numbers
Primes of shape k . 2n + 1
The prime number race
Arithmetic progressions of primes
Consecutive primes in A.P
Cunningham chains
Gaps between primes
Twin primes
Patterns of primes
Gilbreath's conjecture
Increasing and decreasing gaps
Pseudoprimes
Euler pseudoprimes
Strong pseudoprimes
Carmichael numbers
"Good" primes and the prime number graph
Congruent products of consecutive numbers
Gaussian primes
Eisenstein-Jacobi primes
Formulas for primes
The Erd1/4os-Selfridge classi.cation of primes
Values of n making n - 2k prime
Odd numbers not of the form pa 2b
Symmetric and asymmetric primes
Divisibility
Perfect numbers
Almost perfect, quasi-perfect, pseudoperfect, harmonic, weird, multiperfect and hyperperfect numbers
Unitary perfect numbers
Amicable numbers
Quasi-amicable or betrothed numbers
Aliquot sequences
Aliquot cycles
Sociable numbers
Unitary aliquot sequences
Superperfect numbers
Untouchable numbers
Solutions of mo(m) = no(n)
Analogs with d(n), ok(n)
Solutions of o(n) = o(n + 1)
Some irrational series
Solutions of o(q) + o(r) = o(q + r)
Powerful numbers
Exponential-perfect numbers
Solutions of d(n) = d(n + 1)
(m, n + 1) and (m+1, n) with same set of prime factors
The abc-conjecture
Cullen and Woodall numbers
k . 2n + 1 composite for all n
Factorial n as the product of n large factors
Equal products of factorials
The largest set with no member dividing two others
Equal sums of geometric progressions with prime ratios
Densest set with no l pairwise coprime
The number of prime factors of n + k which don''t divide n + i, 0 U i < k
Consecutive numbers with distinct prime factors
Is x determined by the prime divisors of x + 1, x + 2,. . ., x + k?
A small set whose product is square
Binomial coeffcients
Grimm's conjecture
Largest divisor of a binomial coeffcient
If there's an i such that n - i divides _nk_
Products of consecutive numbers with the same prime factors
Euler's totient function
Does o(n) properly divide n - 1?
Solutions of o(m) = o(n)
Carmichael's conjecture
Gaps between totatives
Iterations of o and o
Behavior of o(o(n)) and o(o(n))
Alternating sums of factorials
Sums of factorials
Euler numbers
The largest prime factor of n
When does 2a -2b divide na - nb?
Products taken over primes
Smith numbers
Additive Number Theory
Goldbach's conjecture
Sums of consecutive primes
Lucky numbers
Ulam numbers
Sums determining members of a set
Addition chains
Brauer chains
Hansen chains
The money-changing problem
Sets with distinct sums of subsets
Packing sums of pairs
Modular di.erence sets and error correcting codes
Three-subsets with distinct sums
The postage stamp problem
The corresponding modular covering problem
Harmonious labelling of graphs
Maximal sum-free sets
Maximal zero-sum-free sets
Nonaveraging sets
Nondividing sets
The minimum overlap problem
The n queens problem
Is a weakly indedendent sequence the .nite union of strongly independent ones?
Sums of squares
Sums of higher powers
Diophantine Equations
Sums of like powers
The Fermat problem
Figurate numbers
Waring's problem
Sums of l kth Powers
Sum of four cubes
An elementary solution of x2 = 2y4 1
Sum of consecutive powers made a power
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