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Thread: Number Theory : Order

  1. #1
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    Number Theory : Order

    Hi I have the following question and the solution. I don't quite understand the solution since i'm weak in Number theory. How do I get x=4? Appreciate if i could get step by step workaround or any site that I could refer to

    Number Theory : Order-ord.png
    Last edited by lemma; Jul 22nd 2017 at 09:23 AM.
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  2. #2
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    Re: Number Theory : Order

    The order of any element of the multiplicative group $\mathbb{Z}_{43}^*$

    There are 42 elements of the multiplicative group, so any element will have order 2, 3, 6, 7, 14, 21, or 42. So, any element $g$ such that $g^6\neq 1$ but $g^7=1$ has order 7. Then it is just a matter of trial and error.
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    Re: Number Theory : Order

    Quote Originally Posted by SlipEternal View Post
    The order of any element of the multiplicative group $\mathbb{Z}_{43}^*$

    There are 42 elements of the multiplicative group, so any element will have order 2, 3, 6, 7, 14, 21, or 42. So, any element $g$ such that $g^6\neq 1$ but $g^7=1$ has order 7. Then it is just a matter of trial and error.

    Thanks SlipEternal, but how do i get the order 2, 3, 6, 7, 14, 21, or 42?
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  4. #4
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    Re: Number Theory : Order

    Those are the integer factors of 42.
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