Math 5336 – Number Theory Class activities for September 30, 2002

Dr. Cordero

Topic: Diophantine Equations

  1. Discuss homework from last time.
    1. Practice: §2.2 p.25 # 7, 14
    2. Use the Extended Euclidean Algorithm to find integers x and y such that:
    • 141x+120y=3
    • 243x+41y=1
    • 243x+41y=6
    • 1721x+378y=7
  1. The Stamps Problem
      Suppose you have an unlimited supply of 6 -cents stamps and 11- cents stamps.
    What amounts of postage can you make with these stamps?
    • Solve the Stamps problem.
    • What if the stamps were of 6-cents and 9-cents?
    • What if the stamps were of 6-cents and 10-cents?