Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arithmetic tables ?

  1. Mar 15, 2008 #1
    Arithmetic tables...?!?

    Any help would be v much appreciated!

    Attached Files:

  2. jcsd
  3. Mar 15, 2008 #2
    Are you asking what those tables are? How to read them? How to answer that question in picture?
  4. Mar 15, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    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.
  5. Mar 15, 2008 #4
    What if x is greater then 6 though?


    Aside from trying every possible value of n I'm not sure how to prove n can't be an integer.
  6. Mar 15, 2008 #5
    How can x be greater than 6?
  7. Mar 15, 2008 #6


    User Avatar
    Gold Member

    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.
  8. Mar 16, 2008 #7
    Yes. The subscript on the Z means it's modulo 7 arithmetic.

    That is why I wrote:

    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.
  9. Mar 16, 2008 #8
    So I had some thoughts of n greater then 6. In general any number can be written in modula 7 via the division algorithm

    So if we square x we get:
    Which is equal to 3. Therefore:
    rearranging we get:

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Arithmetic tables ?
  1. Modular arithmetic (Replies: 11)

  2. Modular arithmetic (Replies: 1)

  3. Modular arithmetic (Replies: 4)

  4. Arithmetics in Z (Replies: 3)