1. ## Arithmetic tables...?!?

Hi

Any help would be greatly appreciated!

2. Hello, skywalker!

Given this multiplication table:

. . $\begin{array}{c|ccccccc}
\times & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
2 & 0 & 2 & 4 & 6 & 1 & 3 & 5 \\
3 & 0 & 3 & 6 & 2 & 5 & 1 & 4 \\
4 & 0 & 4 & 1 & 5 & 2 & 6 & 3 \\
5 & 0 & 5 & 3 & 1 & 6 & 4 & 2 \\
6 & 0 & 6 & 5 & 4 & 3 & 2 & 1 \end{array}$

Find the solutions of: $x^2\:=\:3$
. . or explain why there are none.

We want a number $x$ so that: . $x\cdot x \:=\:3$

But we find that:
. . $\begin{array}{ccc}0\cdot0 &=& 0 \\ 1\cdot1 &=&1 \\ 2\cdot2 &=&4 \\ 3\cdot3 &=& 2 \\ 4\cdot4 &=& 2 \\ 5\cdot5 &=& 4 \\ 6\cdot6 &=&1 \end{array}$

There are no cases where: $x\cdot x \:=\:3$
. . Therefore, there are no solutions.