Chapter 1 – Divisibility and Factorization – Homework

• 1.1 – Divisibility:
  pp.9-10: 1(a)(c)(d), 2, 3(a)(c), 5, 6, 7, 9, 10(a)(b)(c), 14(a)(b)(c)
  
• 1.2 – Prime Numbers:
  pp. 17-18: 16(a)(b), 17, 18(a), 20, 21(a), 23, 24, 26, 27, 28, 29
  
• 1.3 – Greatest Common Divisors:
  pp. 21-22: 32(a)(c), 33(a)(b)(c), (35), (41), (43), (44)
  
• 1.4 – The Euclidean Algorithm:
  p.25: 54 (a)(b)(e)(f), 55, 56
  
• 1.5 – The Fundamental Theorem of Arithmetic:
  pp.33-36: 59(a)(c), 60(a)(c), 61(a), 64, 69, 70, 78, 84, 85, 86, 87, 88
  

Chapter 2 – Congruences

• 2.1 – Congruences:
  pp.45-48: 1(a)(b), 2(a)(c), 3(a), 4(a)(c)(e), 11, 13, 14, 15, 18, 19,
  26
  
• 2.2 – Linear Congruences in One Variable:
  p.54: 28(c)(e), 29(d)(f)
  
• 2.3 – The Chinese Remainder Theorem:
  pp.57-58: 33(d)(f), 36
  
• 2.4 – Wilson’s Theorem:
  pp.62-63: 42(f), 43, 44, 45, 47, 48, 49
  
• 2.5 – Fermat’s Little Theorem and Pseudoprimes:
  pp.66-68: 51b)(c), 52, 54(a)(b), 55, 57(b), 58(a)(b), 59, 62, 64
  
• 2.6 – Euler’s Theorem:
  p.72: 68(a)(b), 73, 74, 75
  

Chapter 3 – Arithmetic Functions

• 3.1 – Congruences:
  pp.80-81: 3, 4, 5(e)(f)(g), 6, 7
  
• 3.2 – The Euler Phi-Function:
  pp.84-86: 10(c)(d)(e), 13(a)(d), 14, 15, 20, 23, 26, 27
  
• 3.3 – The Number of Positive Divisors Function:
  pp.88-89: 30(h), 31(e), 32, 40
  
• 3.4 – The Sum of Positive Divisors Function:
  pp.91-92: 42(h), 46, 47, 51
  
• 3.5 – Perfect Numbers:
  p.95: 55, 59
  
• 3.6 – The Mobius Inversion Formula:
  p.100: 64, 65, 66, 67, 68
  

Chapter 4 – Quadratic Residues

• 4.1 – Quadratic Residues:
  pp.106-107: 1(c)(d), 5(a), 6, 7, 8, 10(b)
  
• 4.2 – The Legendre Symbol:
  pp.115-117: 12(b), 13(b), 14(e), 16(a), 17(a), 20, 21, 24, 26, 27
  
• 4.3 – The Law of Quadratic Reciprocity:
  pp.124-125: 28(b)(d)(f), 30, 32, 34, 35, 36