More Divisibility (1.1-1.6)

• Example theorem: If 6 divides an integer n, then 3 also divides n.
  • Walk through the proof. Emphasis on the fact that the proof consists of sentences, not simply equations.
  • Produce similar examples with different numbers.
• Example theorem: If an integer k is congruent to 7 modulo 2, then k is also congruent to 3 modulo 2.
  • Walk through the proof.
  • Produce similar examples with different numbers.
• Theorem 1.1: If a divides b and a divides c, then a also divides the sum of b and c.
• Theorem 1.2: If a divides b and a divides c, then a also divides the difference of b and c.
• Theorem 1.3: If a divides b and a divides c, then a also divides the product of b and c.
• Question 1.4: Can we weaken the hypotheses of theorem 1.3? Can we instead strengthen the conclusion?
• Theorem 1.5: Weakened version of theorem 1.3