### Solution Found!

# 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 \(\mathbf{.}_6\)).

### Questions & Answers

**QUESTION:**

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

**ANSWER:**

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.