(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Letvbe an element of F^{2}_{p}\ {(0,0)}. How many vectors does Span({v}) have? How many 1-dimensional vector subspaces does F^{2}_{p}have?

F^{2}_{p}is the two-dimensional field (a,b) where each a, b are elements of F_{p}, where p is a prime number.

3. The attempt at a solution

I know the total number of elements in the vector space F^{2}_{p}\ {(0,0)} is p^{2}- 1. I also thought that this was the number of vectors in Span({v}) but I've told by a couple people that is not so. I started with the definition of span but I just couldn't see the rest unfold.

Thank you ahead of time for your help.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# How many vectors in span({v})

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