Congruences: Lesson
Lesson 1 of 1
1. 1
Here is a problem people face at work: suppose a team of four must complete a three-task project. Everyone decides to assign the tasks so that everyone works on the same number of tasks. However, t…
2. 2
Good work so far! It turns out that congruences are very much relevant to computer science. If anyone has ever suggested to you that you should encrypt your files using a cipher, then you have indi…
3. 3
Now we will transition into discussing some simple properties that congruences have. We begin by defining the idea that x relates to y if a relationship between inputs x and output y exists. (_Fu…
4. 4
Congratulations, we have proved the reflexive property for congruences! The next property of congruences we will verify is another simple idea called the symmetric property. The symmetric propert…
5. 5
We only have one more property left to show! This final congruence property is called the transitive property, the statement of which goes like this: Suppose we have the integers a, b, c, and n …
6. 6
Now that we have these three properties of congruences defined, we are better prepared for when we need to solve congruence problems! There are three distinct congruence problem types based on whic…
7. 7
Now, we will focus on solving linear congruences, or congruences with the unknown variable contained within a linear expression. Linear expressions are expressions in the form ax + b, where a a…
8. 8
Congratulations, you have reached the end of this lesson! Let’s recap what we learned: - We say that, for integers a, b, and n with n > 0, a is congruent to b mod n if n divides (a-b). Equivalen…

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