How do i know what elements a finite field has??

[pseudo wave]

So i stayed all day to understand finite fields, the videos i watched made sense but i dont understand how do i find the elements of the following finite field. GF(3^2) with the polynom f(x) = x^2 + 1. ?? Please help i have exam in 2 days

[low sparrow]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations

[full fulcrum]

Here's a resource I found that seems helpful
https://www.quora.com/What-is-the-Galois-field-GF-3-2/answer/Alon-Amit?ch=15&oid=262267293

You may check the rest of the answers by clicking the question at the top but they are not guaranteed to be 100% correct, and it may not be beginner friendly

[solar laurel]

Let $f$ be an irreducible polynomial of degree $n$ over $\mathbb{Z}_p[x]$ for some prime $p$. Then $\mathbb{F}:=\mathbb{Z}_p[x]/\langle f\rangle$ is a field with $p^n$ elements

[solar solstice]

omegabet_

[solar laurel]

in general, the number of elements is (number of coefficients)^(degree of polynomial modding out)

finding the elements of F is just computing all remainders when you divide by f, as each remainder forms one of the equivalence classes for congruence mod <f>

[pseudo wave]

okay thanks ! i think i got it

[pseudo wave]

+close