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