| 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 | |
| A p | |
| Table of Contents provided by Publisher. All Rights Reserved. |
