1. ## Modular arithmetic

Can someone please help. I keep getting an assignment back for two problems being worng. Can someone help asap? I am to multiply these 2 problems:

2 ≡ 3 mod 5 and -4 ≡ 1 mod 5
and
-11 ≡ 4 mod 5 and 19 ≡ 1 mod 5

Can someone please help. I keep getting an assignment back for two problems being worng. Can someone help asap? I am to multiply these 2 problems:

2 ≡ 3 mod 5 and -4 ≡ 1 mod 5
and
-11 ≡ 4 mod 5 and 19 ≡ 1 mod 5
There are some signs wrong here. It should be

2 ≡ 3 mod 5 and -4 ≡ 1 mod 5
and
-11 ≡ 4 mod 5 and 19 ≡ 1 mod 5

3. How do you know the signs are wrong? I dont understand this stuff. Multiplying them i dont understand either?

Would the answer be for the first one: -8 ≡ -3 mod 5 simplified to -8 ≡ 2 mod 5???

How do you know the signs are wrong? I dont understand this stuff.
What these equations mean is that the difference between the two sides must be a multiple of 5. I could tell that the first one was wrong because the difference between 2 and 3 is 1, which is not a multiple of 5. But if the equation said 2 ≡ -3 mod 5 then it would be correct, because the difference between 2 and -3 is 5.

Multiplying them i dont understand either?

Would the answer be for the first 1: -8 ≡ -3 mod 5?
Yes.

5. Thank you so much. I got it, I think...Do I have to simplify that answer at all? How do you know when to simplify them? Thank you so much...I am actually understanding this now.

6. ## Still need help

Again my teacher is claiming I am wrong. These two problems are the death of me. My teacher claims they make no sense and they are wrong...I am beginning to think that she is wrong? Someone help me please! And thanks

-11 ≡ 4 mod 5 and 19 ≡ -1 mod 5 2 ≡ -3 mod 5 and -4 ≡ 1 mod 5
-11 * 19 ≡ 4 * -1 mod 5 2 * -4 ≡ -3 * 1 mod 5
-209 ≡ -4 mod 5 -8 ≡ -3 mod 5

Again my teacher is claiming I am wrong. These two problems are the death of me. My teacher claims they make no sense and they are wrong...I am beginning to think that she is wrong? Someone help me please!
Perhaps, you and the instructor are simply experiencing a failure in communication.
Maybe she has a different form in mind. Maybe she wants the answer written in a particular way.
Or maybe she is just wrong.
Below, I have listed the five equivalence classes modulo 5.
You can check your answers. Are they together in the same class?
$\displaystyle \begin{gathered} \left[ 0 \right] = \left\{ { \ldots , - 15, - 10, - 5,0,5,10 \cdots } \right\} \hfill \\ \left[ 1 \right] = \left\{ { \ldots , - 14, - 9, - 4,1,6,11 \cdots } \right\} \hfill \\ \left[ 2 \right] = \left\{ { \ldots , - 13, - 8, - 3,2,7,12 \cdots } \right\} \hfill \\ \end{gathered}$
$\displaystyle \begin{gathered} \left[ 3 \right] = \left\{ { \ldots , - 12, - 7, - 2,3,8,13 \cdots } \right\} \hfill \\ \left[ 4 \right] = \left\{ { \ldots , - 11, - 6, - 1,4,9,14 \cdots } \right\} \hfill \\ \end{gathered}$

8. They are in the same class...1st problem

-11 ≡ 4 mod 5 and 19 ≡ -1 mod 5
-11 * 19 ≡ 4 * -1 mod 5
-209 ≡ -4 mod 5

-209 and -4 are in the class 1.

all the directions stated was to multilpy the congruences

so this is right correct?? what would be another way to right this??