can anyone do this question?

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- Feb 1st 2009, 05:22 AMsrk619logic sets help
can anyone do this question?

- Feb 1st 2009, 05:32 AMRapha
Hey

Do you know what Z6 means? What exactly is your question?

(1*1) mod 6 = 1

(1*2) mod 6 = 2

....

(1*5) mod 6 = 5

(2*1) mod 6 = (1*2) mod 6 = 2

(2*2) mod 6 = 4

(2*3) mod 6 = 6 mod 6 = 0

(2*4) mod 6 = 8 mod 6 = 2

(2*5) mod 6 = 10 mod 6 = 4

....

and so on.

Does it help?

Regards, Rapha - Feb 1st 2009, 05:54 AMSoroban
Hello, srk619!

Rapha is right . . .

You're expected to know what $\displaystyle \mathbb{Z}_6$ means.

If you don't, you shouldn't have been assigned this problem.

Quote:

Give the multiplication table for $\displaystyle \mathbb{Z}_6$

and hence find all solutions to: .$\displaystyle x^2 \,=\,3\:\text{ in }\mathbb{Z}_6$ or explain why there are none.

. . $\displaystyle \begin{array}{c||c|c|c|c|c|c|}

\times & 0&1&2&3&4&5 \\ \hline \hline

0 & 0&0&0&0&0&0 \\ \hline

1 & 0&1&2&3&4&5 \\ \hline

2 & 0&2&4&0&2&4 \\ \hline

3 & 0&3&0&3&0&3 \\ \hline

4 & 0&4&2&0&4&2 \\ \hline

5 & 0&5&4&3&2&1 \\ \hline\end{array}$

The values for $\displaystyle x^2$ are on the main diagonal,

. . where we see that: .$\displaystyle 3\cdot3 \:=\:3\text{ (mod 6)}$

Therefore: .$\displaystyle x = 3$

- Feb 1st 2009, 06:48 AMsrk619
the question is part of Integers, Congruence arithmetic

its something like what is in the diagram