Arithmetic tables ?

1. Mar 15, 2008

*Jas*

Arithmetic tables...?!?

Any help would be v much appreciated!

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2. Mar 15, 2008

rodigee

Are you asking what those tables are? How to read them? How to answer that question in picture?

3. Mar 15, 2008

CRGreathouse

The tables work like ordinary multiplication tables -- choose the row & column of the numbers you're multiplying, then their intersection has the product.

Hint on the questions: the squares are on the diagonal of the multiplication table.

4. Mar 15, 2008

John Creighto

What if x is greater then 6 though?

x^2=3+n*7

Aside from trying every possible value of n I'm not sure how to prove n can't be an integer.

5. Mar 15, 2008

rodigee

How can x be greater than 6?

6. Mar 15, 2008

DaveC426913

Has math changed so much since I was a boy???

Since when does 6+6 = 5?
Since when does 6x6 = 1?

It looks like there's some sort of modulo going on.

7. Mar 16, 2008

John Creighto

Yes. The subscript on the Z means it's modulo 7 arithmetic.
http://en.wikipedia.org/wiki/Modular_arithmetic

That is why I wrote:
x^2=3+n*7

So x could be greater then 6 for a suitably large choice of n but I don't know if it can be an integer.

8. Mar 16, 2008

John Creighto

So I had some thoughts of n greater then 6. In general any number can be written in modula 7 via the division algorithm
x=r+nq

So if we square x we get:
(r+nq)^2=r^2+2rnq+n^2q^2
Which is equal to 3. Therefore:
r^2+2rnq+n^2q^2=3
rearranging we get:
q^2n^2+2rqn+(r^2-3)=0

Now, perhaps someone who knows something of group theory can tell me under what conditions the above polynomial of n, will have integer roots. If we know that condition are we easily able to choose an r and a q that will satisfy this condition?

Last edited: Mar 16, 2008