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Write out the addition and multiplication tables for Z6
Chapter 4, Problem 46E(choose chapter or problem)
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.