# Thread: abstract algebra - group theory

1. ## abstract algebra - group theory

Need help on this. i dont understand the whole equation. I've found some resources that helped me to understand this equation .

2. ## Re: abstract algebra - group theory

Originally Posted by noobpronoobpro
Need help on this. i dont understand the whole equation.
It means that the number $2+_{12}x+_{12}7\equiv 1$. When the LHS is divided by $12$ the remainder is $1$.
The what is $x~?$

3. ## Re: abstract algebra - group theory

Blast! I wrote out an answer but my internet connection went down before I could post it!

"$\displaystyle Z_{12}$" is the set of integers "modulo 12". That is, we consider two integers whose difference is a multiple of 12 to be the same. and "$\displaystyle +_{12}$" is "addition modulo 12". "$\displaystyle 7+_{12} 2= 9$" because 9 is less than 12 but $\displaystyle 7+ 8+_{12}= 3$ because $\displaystyle 7+ 8= 15= 12+ 3$. Here, $\displaystyle 2+_{12} x+_{12}+ 7= x+_{12} 9= 1$ is the same as $\displaystyle x= 1-_{12} 9= -8= -12+ 4= 4$ (mod 12).