Homework for the seventh week: primes, factorization, and modular arithmetic

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.

- Section 5.1 (prime numbers):
- 3, 4, 5, 7
- 14, 15, 16
- 80

- Section 5.1 (factorization):
- 34-36
- 56-59

- Section 5.4 (modular arithmetic):
- 9-13 (this is modulo 5, and the inverse of a is a number b such that a + b ≡ 0\kern 18mu ({\rm mod}\kern 6mu 5))
- 29, 31
- 33, 35, 37, 39

- Section 5.1 (divisibility rules):
- 21-24
- 43-44
- Take a familiar incomplete integer, -679-. Using the expression of -679- as N = 1{0}^{4} ⋅ {x}_{4} + {x}_{0} + 6790, use 8\mathrel{∣}N to find {x}_{0}? Given that, use 9\mathrel{∣}N to find {x}_{4}. Now if 72 turkeys cost $-679-, what is the total?

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.