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
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