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Math Help - Multiplication Table

  1. #1
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    Multiplication Table

    I don't understand what this question actually wants, could anyone shed some light on it for me?

    Give the multiplication table for ℤ6, and hence find all solutions to x [squared] = 3 in ℤ6, or explain why there are none.
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  2. #2
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    Quote Originally Posted by -NM- View Post
    I don't understand what this question actually wants, could anyone shed some light on it for me?

    Give the multiplication table for ℤ6, and hence find all solutions to x [squared] = 3 in ℤ6, or explain why there are none.
    mod 6 multiplication table

    x 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
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  3. #3
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    That is the multiplication table for Z6, but how do you find the soloutions to x [squared] = 3 using it?
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  4. #4
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    looking down the main diagonal of the table ...

    0^2 = 0

    1^2 = 1

    2^2 = 4

    3^2 = 3

    4^2 = 4

    5^2 = 1

    so ... x^2 = 3 , x = \, ?
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  5. #5
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    The possible values for x^2 in Z_6 can be found in the diagonal :

    x 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


    so what is the only x, such that x=3 in Z_6 ?



    (all credits to skeeter for the table XD)
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  6. #6
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    Thank you Moo and Skeeter, so x^2=3 which means that x is the square root of 3.. 1.72?

    Seems very basic now thanks alot
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  7. #7
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    Quote Originally Posted by sally1989 View Post
    Thank you Moo and Skeeter, so x^2=3 which means that x is the square root of 3.. 1.72?

    Seems very basic now thanks alot
    No
    x=3 because 3=3 as already posted by Moo and skeeter
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  8. #8
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    Quote Originally Posted by sally1989 View Post
    Thank you Moo and Skeeter, so x^2=3 which means that x is the square root of 3.. 1.72?
    no ... x = 3, there are no decimals in Z_6
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  9. #9
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    So what exactly is Z6, other than a grid of numbers?

    Apologies for my idiocy
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  10. #10
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    Quote Originally Posted by sally1989 View Post
    So what exactly is Z6, other than a grid of numbers?
    you asked ...

    Multiplicative group of integers modulo n - Wikipedia, the free encyclopedia
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  11. #11
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    Well, looks like im screwed. Everything that I try to learn seems to require some sort of background learning that I dont have, nor do I know what I dont understand - it all looks like a foreign language. Ive got a paper due in soon, and if anyone knows where I can find a website that explains things in a more basic fashion it looks like a fail for me.

    Thankyou for all your help <3
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