# Modular arithmetic

• Sep 15th 2008, 07:10 AM
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
• Sep 15th 2008, 08:42 AM
Opalg
Quote:

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
• Sep 15th 2008, 09:51 AM
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???
• Sep 15th 2008, 10:07 AM
Opalg
Quote:

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.

Quote:

Multiplying them i dont understand either?

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

Yes.
• Sep 15th 2008, 02:01 PM
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.
• Sep 20th 2008, 04:52 AM
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
• Sep 20th 2008, 06:39 AM
Plato
Quote:

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?
$\begin{gathered}
\left[ 0 \right] = \left\{ { \ldots , - 15, - 10, - 5,0,5,10 \cdots } \right\} \hfill \\
\left[ 1 \right] = \left\{ { \ldots , - 14, - 9, - 4,1,6,11 \cdots } \right\} \hfill \\
\left[ 2 \right] = \left\{ { \ldots , - 13, - 8, - 3,2,7,12 \cdots } \right\} \hfill \\
\end{gathered}$

$\begin{gathered}
\left[ 3 \right] = \left\{ { \ldots , - 12, - 7, - 2,3,8,13 \cdots } \right\} \hfill \\
\left[ 4 \right] = \left\{ { \ldots , - 11, - 6, - 1,4,9,14 \cdots } \right\} \hfill \\
\end{gathered}$