# Thread: Number Theory : Order

1. ## 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 2. ## 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.

3. ## Re: Number Theory : Order Originally Posted by SlipEternal 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?

4. ## Re: Number Theory : Order

Those are the integer factors of 42.