RESOURCES
Download PEN extended .
Number Theory Problems from The William Lowell Putnam Mathematics Competition (1980-2006)
Number Theory Problems from IMO Short List (1999-2006)
Here you can obtain the official PEN Problems Book:
1 Introduction 1
2 Divisibility Theory 3
3 Arithmetic in Zn 17
3.1 Primitive Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Quadratic Residues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Primes and Composite Numbers 22
5 Rational and Irrational Numbers 27
5.1 Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2 Irrational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6 Diophantine Equations 33
7 Functions in Number Theory 43
7.1 Floor Function and Fractional Part Function . . . . . . . . . . . . . . . . . . 43
7.2 Divisor Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7.3 Functional Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
8 Sequences of Integers 52
8.1 Linear Recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
8.2 Recursive Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
8.3 More Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
9 Combinatorial Number Theory 62
10 Additive Number Theory 70
11 Various Problems 76
11.1 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
11.2 The Geometry of Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
11.3 Miscellaneous problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
12 References 84
