General Information

Class times: Mon + Wed + Fri from 09:00–09:50 AM [Alpine 212]
Book: Elementary Number Theory, Second Edition (Dover Books on Mathematics); by Underwood Dudley.
Syllabus: Syllabus for Math 102

Instructor: Dr. Joshua Wiscons (he/him/his)
Email: joshua.wiscons@csus.edu
Office: Brighton Hall (BRH) Room 144
Student office hours:

• In person: Mon 2–3 PM and Wed 4–5 PM [Brighton 144]
• Virtual: Thur 12:30–1:30 PM [only via Zoom]
• Also by appointment. Just send me an email.

Homework Assignments

Due dates and submissions are managed in Canvas. Let me know if you have any questions!

Jump to specific assigment: HW01

Homework 01

Problems to submit for grading

These are the problems to turn in. Please organize your work, justify your steps, and write in complete sentences with correct punctuation. Once your finish these problems, please follow the directions in the Canvas assignment to submit them. If you have any questions (about the math or writing or submission process or anything), please let me know!

• Problem 1: Suppose that $a$, $b$, and $c$ are arbitrary integers. Prove that if $a\mid b$ and $b\mid c$, then $a\mid c$.
  • Hint: try to start like this: “Assume that $a\mid b$ and $b\mid c$. Since $a\mid b$, there is some integer $x$ such that $b = ax$. Also since $b\mid c$, there is some integer $y$ such that…” Now keep going to show that $a$ divides $c$; your goal is to show that $c$ is $a$ times some integer.
• Problem 2: Suppose that $a$, $b$, and $d$ are arbitrary integers. Prove that if $d\mid a$ and $d\mid b$, then $d^2\mid ab$.
• Problem 3: Let $a,b\in \mathbb{Z}$ be integers. Prove that if $x^2 + ax + b = 0$ has an integer solution $r$, then $r$ divides $b$.
  • Hint: Try starting like this: “Assume that $x^2 + ax + b = 0$ has an integer solution $r$. Then $r^2 + ar + b = 0$.” Now keep going to show that $r$ divides $b$ according to the definition of divides.
  • Note: the assumption $a,b\in \mathbb{Z}$ only allows you to treat $a$ and $b$ as arbitrary integers, so make sure not to give them specific values.

Problems for extra practice

Please try to solve these problems, but you do not turn them in. I’m happy to talk about these problems (or any others) if you have questions. Problem numbers refer to our book Elementary Number Theory, Second Edition.

• Page 3: Exercise 3
• Page 9: Problem 7