- #1
Bashyboy
- 1,421
- 5
Homework Statement
Consider ##F[x,y]##, where ##F## is some field. I've been working on a problem all day and I'm having trouble with this last step. I am trying to show that ##x \notin(x,y)^n## for any ##n \in \Bbb{N}##.
Homework Equations
The Attempt at a Solution
Note that ##(x,y)^n = [(x)+(y)]^n = \sum_{i=0}^n (x)^i y^{n-i}##. I tried working with this, but I couldn't get anywhere. I could really use a hint; I don't want to have this become a problem that takes two days...