Recent content by Discover85

From my proof we know that for n<4 the polygon is irreducible since n! + 1 != m^2. As for n>5, you can take the derivative and show that the polygon has a minimum less than 0. This contradicts the fact that f(x) = g(x)^2. Thus n = 4.

Yeah, I realized I had reduced it to something fairly ugly when I was using Wolfram and found 7! + 1 fit the bill. I don't know if this helps but this question was posed under the Eisenstiens Criterion section.

Homework Statement Prove that the polynomial $(x-1)(x-2)...(x-n) + 1$ is irreducible over Z for n\geq 1 and n \neq 4Homework Equations N/AThe Attempt at a Solution Let $f(x) = (x-1)(x-2) \cdots (x-n) + 1$ and suppose $f(x) = h(x)g(x)$ for some $h,g \in \mathbb{Z}[x]$ where $\deg(h), \deg(g) <...

Thanks for your help :)

Haha... I'm going to assume you are in my class because this is on my assignment for this week! I had difficulty with it too but I found this which was immensely helpful. Scroll down to proposition 8.3. In the proof they talk about proposition 4.1, which we proved on a previous assignment...

Wouldn't the union of increasing subspaces tend to some infinite subspace?

Would a natural upper bound for this poset be the subspace U such that U contains X and V-{W-X}?

Homework Statement Suppose that V is a vector space, W and X are subspaces with X contained in W. Show that there is a subspace U of V which is maximal subject to the property that U intersect W equals X.Homework Equations N/AThe Attempt at a Solution I know this uses Zorn's Lemma but I can't...