---
tags: mth350, dailyprep
---

# Daily Prep 2B -- MTH 350-01

## Overview

Last time, we defined what it means for an integer to *divide* another integer and began a proof of the *Division Algorithm*. In Module 2B we will complete this proof and introduce the central concept of **integer congruence**.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

* Define what it means for two integers to be congruent modulo $n$; use the definition to decide if two integers are congruent mod $n$ and to rephrase a congruence relationship.
* State and apply Theorem 2.10.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

+ Explain line-by-line the proof of the Division Algorithm.
+ Prove properties of congruence mod $n$ (such as in Activity 2.12).

## Resources for learning

**Reading:** Read through Investigation 2, pages 17-20 in the textbook.

**Video:** Watch the following videos, total running time 27:10.

+ Integer congruence (9:27) https://youtu.be/_-ZMdsQyIJw
+ Reducing an integer modulo $n$ (9:43) https://youtu.be/SO6l6sDwEFg
+ Proofs involving integer congruence (8:00) https://youtu.be/Vfz3EN6U2sc

## Exercises

The exercises for this Daily Prep are found on the Google Form:

https://docs.google.com/forms/d/e/1FAIpQLSdzMPahWcwBGiHqL0kVcXyafZM_9DrAyv3xclyeCMz0-mk_zg/viewform

## Submission and grading

To submit your work, simply submit the Google Form. You will receive a receipt via email to confirm your submission. (Look in your spam folders if you do not see the receipt.)

A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.

[](https://hackmd.io/4b096bEnTXWWRWUOyR995g)

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