Number theory for mathematical contests

Santos D.

Table of contents :
4. MODIFICATIONS……Page 3
10. FUTURE REVISIONS OF THIS LICENSE……Page 4
Preface……Page 7
Well-Ordering……Page 8
Mathematical Induction……Page 10
Practice……Page 14
Fibonacci Numbers……Page 16
Practice……Page 18
Pigeonhole Principle……Page 19
Practice……Page 21
Divisibility……Page 24
Practice……Page 25
Division Algorithm……Page 26
Practice……Page 27
Some Algebraic Identities……Page 28
Practice……Page 30
Congruences……Page 33
Practice……Page 37
Divisibility Tests……Page 38
Practice……Page 39
Practice……Page 40
GCD and LCM……Page 41
Practice……Page 45
Primes……Page 46
Fundamental Theorem of Arithmetic……Page 48
Practice……Page 52
Euclidean Algorithm……Page 55
Practice……Page 57
Linear Congruences……Page 58
A theorem of Frobenius……Page 59
Practice……Page 61
Chinese Remainder Theorem……Page 62
Practice……Page 63
Greatest Integer Function……Page 64
Practice……Page 67
De Polignac’s Formula……Page 69
Complementary Sequences……Page 71
Practice……Page 72
Arithmetic Functions……Page 73
Practice……Page 75
Euler’s Function. Reduced Residues……Page 76
Practice……Page 79
Multiplication in Zn……Page 80
Möbius Function……Page 82
Practice……Page 83
Theorems of Fermat and Wilson……Page 85
Practice……Page 87
Euler’s Theorem……Page 88
Practice……Page 90
The Decimal Scale……Page 91
Practice……Page 93
Non-decimal Scales……Page 94
Practice……Page 95
A theorem of Kummer……Page 96
Miscellaneous Problems……Page 98
Practice……Page 100