I think that I mentioned in another post that I have been playing around with multiplication tables. They make neat pictures and really handsome tablecloth patterns as well as matching place mats. The below picture is a multiplication table mod 257 that I made in Excel. Cool pattern if you click on it to enlarge it and look at it...
The really interesting - not that they make cool place mats but that the numbers all end up being what they are (cool if you are a geek). When you make a multiplication table like this using a modulus that is prime the rows of the table (or columns) end up being permutations of all the possible numbers in the field (modulus - 1). Below is a multiplication table mod 5 without the 0's row / column because those are all 0's obviously.
1 2 3 4
1 1 2 3 4
2 2 4 1 3
3 3 1 4 2
4 4 3 2 1
I'll write more about this later if I feel like it.
HERE is a link to more about this stuff with a fun table that you can put in your own modulus and choose which operator you are interested in (+ - X /). HERE is a link to the home page for that link that has a lot of interesting math related puzzles and other fun stuff.
Anyway that is about it... more later.