Homework Problems

 Section Problems 1.3 Mathematical Induction 7, 8, 18 1.4 Fibonacci Numbers 14 1.5 Divisibility 14, 16, 28, 29, 32 3.1 Prime Numbers 5, 6 3.2 Distribution of Primes 14 3.3 Greatest Common Divisors 5, 6, 16, 18, 24, 30 3.4 Euclidean Algorithm 2 b), 5 b), 7 b) 3.5 Fundamental Theorem of Arithmetic 7, 10, 17, 18, 19, 21, 34 3.6 Factorization Methods & Fermat Numbers 2 a), 3 b), d), 20 3.7 Linear Diophantine Equations 1 a), b), c), d), 2 a), 18 4.1 Introduction to Congruences 5, 9, 25, 28, 29, 30, 34 4.2 Linear Congruences 1 a), b), 6, 8, 12 4.3 Chinese Remainder Theorem 1, 3 5.2 The Perpetual Calendar 1, 2 d), j), o), 3, 6 6.1 Wilson's Theorem & Fermat's Little Theorem 5, 11, 16, 20, 28, 30, 48 6.2 Pseudoprimes 4, 5, 8 6.3 Euler's Theorem 2, 4, 8, 11c) 7.1 Euler's Phi-Function 2 e), 5, 11, 12, 16, 17, 26 7.2 Sum and Number of Divisors 1 c), 2 c), 3, 4, 5 a), 6 e), 8, 9, 12, 40 7.3 Perfect Numbers & Mersenne Primes 4 a), 25, 26 7.4 Möbius Inversion 1 e), f), 14, 15, 16 a), 30, 31, 32 9.1 Order of Integers & Primitive Roots 1 b), 6 c), 8, 14, 18, 20 9.2 Primitive Roots for Primes 5, 10, 11 9.3 Existence of Primitive Roots 5 a), 9, 12, 13, 14 9.4 Discrete Logarithms & Index Arithmetic 3 a), 8, 9, 10 11.1 Quadratic Residues and Nonresidues 1 b), 4, 7, 10, 28 a) 11.2 Law of Quadratic Reciprocity 1 a), c), f), 4, 6