[
  {
    "number": "1.6.1",
    "first_line": "1.6.1. Complete the following sketch of a proof of Proposition 1.6.7 using"
  },
  {
    "number": "1.6.2",
    "first_line": "1.6.2. Prove Proposition 1.6.9. Hint: For part (b), you have to show that"
  },
  {
    "number": "1.6.3",
    "first_line": "1.6.3. Suppose that a natural number p > 1 has the property that for all"
  },
  {
    "number": "1.6.4",
    "first_line": "1.6.4. For each of the following pairs of numbers m; n, compute"
  },
  {
    "number": "1.6.5",
    "first_line": "1.6.5. Show that for nonzero integers m and n, g:c:d:.m; n/               D"
  },
  {
    "number": "1.6.6",
    "first_line": "1.6.6. Show that for nonzero integers m and n, g:c:d:.m; n/ is the largest"
  },
  {
    "number": "1.6.7",
    "first_line": "1.6.7. Show that if p is a prime number and a is any nonzero integer, then"
  },
  {
    "number": "1.6.8",
    "first_line": "1.6.8. Suppose that a and b are relatively prime integers and that x is an"
  },
  {
    "number": "1.6.9",
    "first_line": "1.6.9. Show that if a prime number p divides a product a1 a2 : : : ar of"
  },
  {
    "number": "1.6.10",
    "first_line": "1.6.10."
  },
  {
    "number": "1.6.11",
    "first_line": "1.6.11. Let n1 ; : : : ; nk be nonzero integers. Let d D g:c:d.n1 ; : : : ; nk /,"
  },
  {
    "number": "1.6.12",
    "first_line": "1.6.12. Let n1 ; : : : ; nk be nonzero integers."
  },
  {
    "number": "1.6.13",
    "first_line": "1.6.13."
  },
  {
    "number": "1.6.14",
    "first_line": "1.6.14. Show two nonzero integers are relatively prime if and only if they"
  },
  {
    "number": "1.6.15",
    "first_line": "1.6.15. Prove Lemma 1.6.26. You may use the uniqueness of the prime"
  }
]