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1.

図書

図書
Goro Shimura
出版情報: Berlin : Springer-Verlag, 1968  69 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 54
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2.

図書

図書
dargestellt von Paul Bachmann
出版情報: Leipzig : B.G. Teubner, 1926  xxii, 548 p. ; 22 cm
シリーズ名: Zahlentheorie ; 5. Teil
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3.

図書

図書
M.R. Schroeder
出版情報: Berlin ; Tokyo : Springer-Verlag, c1986  xix, 374 p. ; 24 cm
シリーズ名: Springer series in information sciences ; 7
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4.

図書

図書
by Ross Honsberger
出版情報: [Washington, D.C.] : Mathematical Association of America, c1973-c1985  3 v. ; 23 cm
シリーズ名: The Dolciani mathematical expositions ; no. 1-2, 9
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目次情報: 続きを見る
Gleanings from combinatorics / 1:
Gleanings from geometry / 2:
Two problems in combinatorial geometry / 3:
Sheep fleecing with Walter Funkenbusch / 4:
Two problems in graph theory / 5:
Two applications of generating functions / 6:
Some problems from the Olympiads / 7:
A second look at the Fibonacci and Lucas numbers / 8:
Some problems in combinatorics / 9:
Four clever schemes in cryptography / 10:
Gleanings from number theory / 11:
Schur's theorem: an application of Ramsey's theorem / 12:
Two applications of Helly's theorem / 13:
An introduction to Ramanujan's highly composite numbers / 14:
On sets of points in the plane / 15:
Two surprises from algebra / 16:
A problem of Paul Erd÷s / 17:
Cai Mao-Cheng's solution to Katona's problem on families of separating subsets / 18:
Three surprises from combinatorics and number theory
Four minor gems from geometry
A problem in checker-jumping
The generation of prime numbers
Two combinatorial proofs
Bicentric polygons, Steiner chains, and the hexlet
A theorem of Gabriel Lame
Box-packing problems
A theorem of Bang and the isosceles tetrahedron
An intriguing series
Chavatal's art gallery theorem
The set of distances determined by n points in the plane
A Putnam paper problem
Lovasz' proof of a theorem of Tutte
Gleanings from combinatorics / 1:
Gleanings from geometry / 2:
Two problems in combinatorial geometry / 3:
5.

図書

図書
by Daniel Shanks
出版情報: New York, N.Y. : Chelsea Pub. Co., c1985  xiii, 304 p. ; 24 cm
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目次情報: 続きを見る
From Perfect Numbers to the Quadratic Reciprocity Law / Chapter I:
Perfect numbers / 1:
Euclid / 2:
Euler's converse proved / 3:
Euclid's algorithm / 4:
Cataldi and others / 5:
The prime number theorem / 6:
Two useful theorems / 7:
Fermat and others / 8:
Euler's generalization proved / 9:
Perfect numbers, II / 10:
Euler and $M_{31}$ / 11:
Many conjectures and their interrelations / 12:
Splitting the primes into equinumerous classes / 13:
Euler's criterion formulated / 14:
Euler's criterion proved / 15:
Wilson's theorem / 16:
Gauss's criterion / 17:
The original Legendre symbol / 18:
The reciprocity law / 19:
The prime divisors of $n^2 +a$ / 20:
The Underlying Structure / Chapter II:
The residue classes as an invention / 21:
The residue classes as a tool / 22:
The residue classes as a group / 23:
Quadratic residues / 24:
Is the quadratic reciprocity law a deep theorem? / 25:
Congruential equations with a prime modulus / 26:
Euler's $\phi$ function / 27:
Primitive roots with a prime modulus / 28:
$\mathfrak{M}_{p}$ as a cyclic group / 29:
The circular parity switch / 30:
Primitive roots and Fermat numbers / 31:
Artin's conjectures / 32:
Questions concerning cycle graphs / 33:
Answers concerning cycle graphs / 34:
Factor generators of $\mathfrak{M}_{m}$ / 35:
Primes in some arithmetic progressions and a general divisibility theorem / 36:
Scalar and vector indices / 37:
The other residue classes / 38:
The converse of Fermat's theorem / 39:
Sufficient conditions for primality / 40:
Pythagoreanism and Its Many Consequences / Chapter III:
The Pythagoreans / 41:
The Pythagorean theorem / 42:
The $\sqrt 2$ and the crisis / 43:
The effect upon geometry / 44:
The case for Pythagoreanism / 45:
Three Greek problems / 46:
Three theorems of Fermat / 47:
Fermat's last "Theorem" / 48:
The easy case and infinite descent / 49:
Gaussian integers and two applications / 50:
Algebraic integers and Kummer's theorem / 51:
The restricted case, Sophie Germain, and Wieferich / 52:
Euler's "Conjecture" / 53:
Sum of two squares / 54:
A generalization and geometric number theory / 55:
A generalization and binary quadratic forms / 56:
Some applications / 57:
The significance of Fermat's equation / 58:
The main theorem / 59:
An algorithm / 60:
Continued fractions for $\sqrt N$ / 61:
From Archimedes to Lucas / 62:
The Lucas criterion / 63:
A probability argument / 64:
Fibonacci numbers and the original Lucas test Appendix to Chapters I-III: Supplementary comments, theorems, and exercises / 65:
Progress / Chapter IV:
Chapter I fifteen years later / 66:
Artin's conjectures, II / 67:
Cycle graphs and related topics / 68:
Pseudoprimes and primality / 69:
Fermat's last "Theorem," II / 70:
Binary quadratic forms with negative discriminants / 71:
Binary quadratic forms with positive discriminants / 72:
Lucas and Pythagoras / 73:
The progress report concluded / 74:
The second progress report begins / 75:
On judging conjectures / 76:
On judging conjectures, II / 77:
Subjective judgement, the creation of conjectures and inventions / 78:
Fermat's last "Theorem," III / 79:
Computing and algorithms / 80:
$\scr{C}(3)\times\scr{C}(3)\times\scr{C}(3)\times\scr{C}(3)$ and all that / 81:
1993 Appendix: Statement on fundamentals Table of definitions / 82:
References
Index
From Perfect Numbers to the Quadratic Reciprocity Law / Chapter I:
Perfect numbers / 1:
Euclid / 2:
6.

図書

図書
Władysław Narkiewicz
出版情報: Warszawa : Pwn-Polish Scientific Pub., 1986  363 p. ; 25 cm
シリーズ名: Monografie matematyczne ; tom 62
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7.

図書

図書
Richard Bellman
出版情報: Reading, Mass. : Benjamin/Cummings Pub. Co., Advanced Book Program, 1980  xvi, 195 p. ; 25 cm
シリーズ名: Mathematics lecture note series ; 57
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8.

図書

図書
by Oystein Ore
出版情報: New York : McGraw-Hill, 1948  x, 370 p. ; 21 cm
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9.

図書

図書
Wacław Sierpiński : translated from Polish by A. Hulanicki
出版情報: Warszawa : Państwowe Wydawn. Naukowe, 1964  480 p. ; 25 cm
シリーズ名: Monografie matematyczne ; t. 42
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10.

図書

図書
by Hans Rademacher
出版情報: New York : Blaisdell Pub. Co., c1964  ix, 146 p. ; 24 cm
シリーズ名: A Blaisdell book in the pure and applied sciences
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