Does modular arithmetic have different rules for different cases?

Then use the fact that (x mod 2pi)=x-2pi or x-4pi respectively, where x is either (a+b) or (2a+2b).In summary, the conversation is about trying to prove an isomorphism problem involving modular arithmetic. The problem solver is not familiar with modular arithmetic and is asking for help, specifically for some identities or references. The suggested solution is to break the problem into cases and use the fact that (x mod 2pi) is equal to x-2pi or x-4pi depending on the range of x.
  • #1
Bipolarity
776
2

Homework Statement


I'm trying to prove the following (as part of an isomorphism problem).
The problem is I don't know much about modular arithmetic, so would appreciate some help.

[tex] 2((a+b)mod \ 2π) = (2a+2b)mod \ 4π. [/tex]

given that a,b are both nonnegative and less than 2π.

Homework Equations


The Attempt at a Solution


I believe there are certain identities for modular arithmetic that I could use, but do not know. Can anyone tell me some or give me a link to some modular arithmetic identities? Thanks.

BiP
 
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  • #2
Bipolarity said:

Homework Statement


I'm trying to prove the following (as part of an isomorphism problem).
The problem is I don't know much about modular arithmetic, so would appreciate some help.

[tex] 2((a+b)mod \ 2π) = (2a+2b)mod \ 4π. [/tex]

given that a,b are both nonnegative and less than 2π.


Homework Equations





The Attempt at a Solution


I believe there are certain identities for modular arithmetic that I could use, but do not know. Can anyone tell me some or give me a link to some modular arithmetic identities? Thanks.

BiP

Break it into cases i) 0<=(a+b)<2pi and ii) 2pi<=(a+b)<4pi.
 

Related to Does modular arithmetic have different rules for different cases?

1. What is modular arithmetic?

Modular arithmetic is a type of arithmetic that deals with integers and their remainders after division by a fixed number, called the modulus. It is often used in number theory, cryptography, and computer science.

2. How is modular arithmetic used in proofs?

Modular arithmetic can be used in proofs to show that two numbers are congruent, or have the same remainder when divided by a fixed number. This is useful in proving certain properties of numbers or in solving equations.

3. What is a modular arithmetic proof?

A modular arithmetic proof is a type of mathematical proof that uses modular arithmetic to show that a statement or theorem is true. It involves manipulating equations and using properties of modular arithmetic to arrive at a conclusion.

4. What are some common properties used in modular arithmetic proofs?

Some common properties used in modular arithmetic proofs include the distributive property, the associative and commutative properties, and the cancellation property. These properties allow for the manipulation of equations in a modular system.

5. Can modular arithmetic be used to prove all mathematical statements?

No, modular arithmetic is limited to dealing with integers and their remainders, so it cannot be used to prove all mathematical statements. It is most effective in proving properties of numbers and solving equations in a modular system.

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