# Modular arithmetic proof

1. Mar 21, 2013

### Bipolarity

1. The problem statement, all variables and given/known data
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.

$$2((a+b)mod \ 2π) = (2a+2b)mod \ 4π.$$

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

2. Relevant equations

3. 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

2. Mar 21, 2013

### Dick

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