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

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 Microsoft^{TM} 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.