Number Theory: An Introduction to Mathematics

...

...

Universitext Forothertitlesinthisseries,goto http://www.springer.com/series/ ...

W.A. Coppel Number Theory An Introduction to Mathematics Second Edition ...

...

W.A. Coppel 3 Jansz Crescent 2603 Griffith Australia (^) ISBN 978-0-387-89485-0 e-ISBN 978-0-387-89486- DOI 10.1007/978-0-387-89 ...

For Jonathan, Nicholas, Philip and Stephen ...

Contents Preface to the Second Edition....................................... xi ...

...

Contents ix ...

I The Expanding Universe of Numbers............................ Part A 0 Sets,RelationsandMappings 1 NaturalNumbers............ ...

Preface to the Second Edition Undergraduate courses in mathematics are commonly of two types. On the one hand there are courses ...

xii Preface and refer back to it later as required. Chapter V, on Hadamard’s determinant problem, shows that elementary number t ...

Preface xiii The theory of numbers provides ample evidence that topics pursued for their own intrinsic interest can later find s ...

...

I The Expanding Universe of Numbers For many people, numbers must seem to be the essence of mathematics.Number theory, which is ...

2 I The Expanding Universe of Numbers We will not formally define aset, but will simply say that it is a collection of objects, ...

0 Sets, Relations and Mappings 3 It is easily seen that union and intersection have the following algebraic properties: A∪A=A, A ...

4 I The Expanding Universe of Numbers reflexiveifaRafor everya∈A; symmetricifbRawheneveraRb; transitiveifaRcwheneveraRbandbRc. I ...

1 Natural Numbers 5 unique and equal. Thus, for any bijective mapf:A→B, there is a uniqueinverse mapf−^1 :B→Asuch thatf−^1 ◦f=iA ...