Solved and unsolved problems in number theory

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Solved and unsolved problems in number theory / by Daniel Shanks

版:: 3rd ed
資料種別:: 図書
出版情報:: New York, N.Y. : Chelsea Pub. Co., c1985
形態:: xiii, 304 p. ; 24 cm
著者名:: Shanks, Daniel, 1917- <DA01298473>
ISBN:: 9780828412971 [0828412979]
書誌ID:: BA00724401

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Solved and unsolved problems in number theory. 2nd ed
by Daniel Shanks , Chelsea Pub. Co. , c1978

書誌詳細

その他の標題:

Number theory

注記:

Spine title: Number theory
Originally published 1962; 2nd ed. 1978
Bibliography: p. 283-299
Includes index

主題:

Numbers, Theory of

言語:

英語

目次情報:

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：

Euler's converse proved / 3：

Euclid's algorithm / 4：

Cataldi and others / 5：

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