1. ## Multiplication Table

I don't understand what this question actually wants, could anyone shed some light on it for me?

Give the multiplication table for ℤ6, and hence find all solutions to x [squared] = 3 in ℤ6, or explain why there are none.

2. Originally Posted by -NM-
I don't understand what this question actually wants, could anyone shed some light on it for me?

Give the multiplication table for ℤ6, and hence find all solutions to x [squared] = 3 in ℤ6, or explain why there are none.
mod 6 multiplication table

x 0 1 2 3 4 5
0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2 4 0 2 4
3 0 3 0 3 0 3
4 0 4 2 0 4 2
5 0 5 4 3 2 1

3. That is the multiplication table for Z6, but how do you find the soloutions to x [squared] = 3 using it?

4. looking down the main diagonal of the table ...

$\displaystyle 0^2 = 0$

$\displaystyle 1^2 = 1$

$\displaystyle 2^2 = 4$

$\displaystyle 3^2 = 3$

$\displaystyle 4^2 = 4$

$\displaystyle 5^2 = 1$

so ... $\displaystyle x^2 = 3$, $\displaystyle x = \, ?$

5. The possible values for x^2 in Z_6 can be found in the diagonal :

x 0 1 2 3 4 5
0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2 4 0 2 4
3 0 3 0 3 0 3
4 0 4 2 0 4 2
5 0 5 4 3 2 1

so what is the only x, such that x²=3 in Z_6 ?

(all credits to skeeter for the table XD)

6. Thank you Moo and Skeeter, so x^2=3 which means that x is the square root of 3.. 1.72?

Seems very basic now thanks alot

7. Originally Posted by sally1989
Thank you Moo and Skeeter, so x^2=3 which means that x is the square root of 3.. 1.72?

Seems very basic now thanks alot
No
x=3 because 3²=3 as already posted by Moo and skeeter

8. Originally Posted by sally1989
Thank you Moo and Skeeter, so x^2=3 which means that x is the square root of 3.. 1.72?
no ... x = 3, there are no decimals in $\displaystyle Z_6$

9. So what exactly is Z6, other than a grid of numbers?

Apologies for my idiocy

10. Originally Posted by sally1989
So what exactly is Z6, other than a grid of numbers?