Another integers mod 4 question

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In summary, integers mod 4 involves looking at the remainder when a number is divided by 4, with possible values ranging from 0 to 3. Calculations with integers mod 4 use the same operations as regular integers, but the result must always be reduced to a value between 0 and 3. Integers mod 4 have a variety of applications in fields such as cryptography and computer science, and a common problem involving them is finding the remainder when a large number is divided by 4. The main difference between integers mod 4 and regular integers is the limited number of possible values and different operation rules in the mod 4 system.
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DanielThrice
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Use the first isomorphism theorem to show the following:

Z/(4Z) is isomorphic to Z4.

There are other ones to solve I'm just using this as an example so I can figure out the thinking behind it. I can prove it with multiplication tables, but in reference to the F.I.T. I'm not sure how to start.
 
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  • #2
What is Z4? Do you mean C4 (the cyclic group of 4 elements)

What is the first isomorphism theorem?
 

Related to Another integers mod 4 question

1. What is the concept of integers mod 4?

The concept of integers mod 4 involves dividing a number by 4 and looking at the remainder. This remainder can be any number from 0 to 3, which represents the different possible values in the mod 4 system.

2. How do you perform calculations with integers mod 4?

To perform calculations with integers mod 4, you can use the same operations as with regular integers, but you must always take the remainder of the result when divided by 4. For example, 5 + 6 = 11, but in integers mod 4, it would be written as 1 + 2 = 3 (11 mod 4 = 3).

3. What are the applications of integers mod 4?

Integers mod 4 have various applications in fields such as cryptography, computer science, and number theory. It is often used in coding and error detection as well as in creating secure algorithms.

4. Can you give an example of a problem involving integers mod 4?

One example of a problem involving integers mod 4 is finding the remainder when a large number is divided by 4. For instance, if we have the number 582, the remainder when divided by 4 is 2. This can be written as 582 mod 4 = 2.

5. What is the difference between integers mod 4 and regular integers?

The main difference between integers mod 4 and regular integers is that in the mod 4 system, there are only four possible values (0, 1, 2, 3), whereas regular integers have an infinite number of values. Additionally, operations in integers mod 4 follow different rules compared to regular integers, as the result must always be reduced to a value between 0 and 3.

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