文档介绍：PROBLEMS IN ELEMENTARY NUMBER THEORY
Hojoo Lee, Version [2003/11/24]
God does arithmetic. Gauss
Contents
1. Preface 2
2. Notations and Abbreviations 3
3. Divisibility Theory I 4
4. Divisibility Theory II 8
5. Arithmetic in Zn 11
6. Primes posite Numbers 13
7. Rational and Irrational Numbers 15
8. Diophantine Equations I 18
9. Diophantine Equations II 21
10. Functions in Number Theory 23
11. Sequences of Integers 26
12. Combinatorial Number Theory 31
13. Additive Number Theory 35
14. The Geometry of Numbers 38
15. Miscellaneous Problems 39
16. Sources 41
17. References 53
1
2 PROBLEMS IN ELEMENTARY NUMBER THEORY
1. Preface
The heart of Mathematics is its problems. Paul Halmos
1. Introduction The purpose of this book is to present a collection of
interesting questions in Number Theory. Many of the problems are math-
petition problems all over the world including IMO, APMO,
APMC, Putnam, etc. I have given sources of the problems at the end of the
book. The book is available at
/∼ideahitme/
2. How You Can Help This is an unfinished manuscript. I would
greatly appreciate hearing about any errors in the book, even minor ones. I
also would like to hear about
a) challenging problems in Elementary Number Theory,
b) interesting problems concerned with the History of Num-
ber Theory,
c) beautiful results that are easily stated,
d) remarks on the problems in the book.
You can send ments to the author at hojoolee@ .
3. Acknowledgments The author would like to thank the following
people for sending me suggestions and corrections, etc. : Arne Smeets
(Belgium), Ha Duy Hung (Vietnam), Leonid G. Fel (Israel), and Orlando
Doehring (Germany)
PROBLEMS IN ELEMENTARY NUMBER THEORY 3
2. Notations and Abbreviations
Notations
Z is the set of integers
N is the set of positive integers
N0 is the set of nonnegative integers
Pm|n n is a multipleP of m.
d|n f(d) = d∈D(n) f(d) (D(n) = {d ∈ N : d|n})
[x]