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## Homework Statement

Show that n

^{2 [tex]\neq[/tex]}2 (mod6) for all

**n**in Z

## Homework Equations

## The Attempt at a Solution

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**

I did only the table for mod 6 and then I don't have an idea what to do.

I am not even sure if I understand what exactly I have to do with this problem.

Please help me if you can.

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