MA-410 Homework 2

Due at 4:59pm in my mailbox in SAS 3151, Thursday, March 5, 2015

All solutions must be submitted stapled in hardcopy either to me in class or placed in my mailbox.
Note my office hours on my schedule.

1. Please prove for all composite integers n ≥ 4 that (10ⁿ - 1)/9 is a composite integer. That's an integer which in radix 10 has n 1-digits.
2. Please prove that there are infinitely many primes that are congruent 5 (modulo 6). [Hint: Suppose there are finitely many. Let Q be the product of all such primes. Consider the prime factors of N = 3Q + 2. Take all modulo 6.]
3. ENT, §4.2, Problem 15, page 68.
4. ENT, §4.4, Problem 15, (c) only, page 83.
5. ENT, §4.4, Problem 20, (c) only, page 84.
6. ENT, §5.2, Problem 19, page 93.