## Chapter 25Homework for the seventh week: primes, factorization, and modular arithmetic

### 25.1 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.

• 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 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.