Homework 1

This assignment is due by the beginning of class on Friday, January 30th. Be sure to review the homework guidelines before getting started.

• Prove that for any $n \in \mathbb{Z}$ and any positive integer k, at least one number from the set $\{n,n+1,\cdots, n+k-1\}$ is divisible by k.
• Prove that if a,b and c are integers satisfying $a \mid b$ and $a \nmid c$, then $a \nmid b+c$.
• From Strayer, do the following problems:
• 2
• 3(b,d)
• 5
• 11(b),(d)
• 13
• 32(f)
• 33(d)
• 36(a)
• 54(f)

If you want some extra practice on problems from these sections, here are a few suggestions. You do *not* need to turn these in.

• Suppose that a is a nonzero integer and d is an integer so that $d \mid a$. Prove that $|d| \leq |a|$.
• From Strayer, Chapter 1: 3(a,c,e,f), 10(a,c), 12, 42, 54(a-e), 55