## Chapter 28Homework for the eighth week: GCD, LCM, ax + by = c

### 28.1 Homework

Notes also available as PDF.

Practice is absolutely critical in this class.

Groups are fine, turn in your own work. Homework is due in or before class on Mondays.

• Exercises 5.3:
• 62, 66, 70
• Compute the following using both the prime factorization method and the Euclidean algorithm:
• (720,241)
• (64,336)
• (-15,75)
• Compute the least common multiples:
• \mathop{lcm}\nolimits (64,336)
• \mathop{lcm}\nolimits (11,17)
• \mathop{lcm}\nolimits (121,187)
• \mathop{lcm}\nolimits (2025,648)

Postponed:

• Find two integer solutions to each of the following, or state why no solutions exist:
• 64x + 336y = 32
• 33x - 27y = 11
• 31x - 27y = 11

Note that you may email homework. However, I don’t use MicrosoftTM products (e.g. Word), and software packages are notoriously finicky about translating mathematics.

If you’re typing it (which I advise just for practice in whatever tools you use), you likely want to turn in a printout. If you do want to email your submission, please produce a PDF or PostScript document.