# Write out the addition and multiplication tables for Z6

Chapter 4, Problem 46E

(choose chapter or problem)

QUESTION:

Write out the addition and multiplication tables for $$\mathbf{Z}_{6}$$ (where by addition and multiplication we mean $$\mathbf{+}_6$$ and $$\mathbf{.}_6$$).

QUESTION:

Write out the addition and multiplication tables for $$\mathbf{Z}_{6}$$ (where by addition and multiplication we mean $$\mathbf{+}_6$$ and $$\mathbf{.}_6$$).

Step 1 of 3

In this problem we have to write the addition and multiplication table for  .where, by addition means  and by multiplication means  .

Arithmetic  operations can be defined on  as, the set of non-negative integers less than m,

that is, the set {0, 1,...,m ? 1}.

In mathematical form, we define addition of these integers, denoted by  by

a  b = (a + b) mod m,

where the addition on the right-hand side of this equation is the ordinary addition of integers.

and

we define multiplication of these integers, denoted by  by

a  b = (a · b) mod m,

where the multiplication on the right-hand side of this equation is the ordinary multiplication of

integers. The operations  and  are called addition and multiplication modulo m.