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May
4
comment In how many different ways can the faces of a regular dodecahedron be colored?
Nice. As noted in the comments on the original question, the numerical sequence is tabulated at the OEIS.
May
4
comment What type of graph is this?
There is such a thing as a balanced graph; at captura.uchile.cl/bitstream/handle/2250/5429/… a graph is called balanced when its clique matrix is balanced. But it seems unlikely that whoever set the question had this in mind.
May
4
comment dividing planar regions into congruent parts
I note that you have used the hypothesis about the area being finite. Is there a counterexample with infinite area?
May
4
comment The way to prove that a polynomial is irreducible
If the field has $2^{1000}$ elements, it may not be so easy to check whether the polynomial has a root. On the other hand, if the field is the rationals, and the first and last coefficients aren't too big, it's easy to check whether the polynomial has a root.
May
4
comment Examples on the dimension of vector spaces of real functions
Adam, you start out by saying $S$ is a space of functions from ${\bf R}^n$ to $\bf R$, and all your examples are functions from ${\bf R}^n$ to $\bf R$, so maybe it's not surprising that your question about $f_1\circ f_2$ seems impossible.
May
4
comment Normal subgroup of a normal subgroup
I would imagine that someone asking this sort of question is unlikely to know what a solvable group is.
May
4
comment The way to prove that a polynomial is irreducible
And for polynomials of degrees 2 and 3, it doesn't matter whether the field is finite or not.
May
4
comment The way to prove that a polynomial is irreducible
When you write "not detachable", do you mean "irreducible"? When you write "final", do you mean "finite"?
May
4
comment Normal subgroup of a normal subgroup
There are examples in the group of symmetries of the square (the 8-element dihedral group).
May
4
comment Examples on the dimension of vector spaces of real functions
Is there any reason to think that the set of compositions is a vector space?
May
4
comment continuous rational value function in R
Continuous functions on the reals have the intermediate value property; if they take on the values $a$ and $b$ then they take on every value between $a$ and $b$.
May
4
comment A basic question on factorization
I think you have proved (in the paragraph starting, A connection to the statement) that $\Phi_p(x/2^{1/p})$ is irreducible over ${\bf Q}(2^{1/p})$.
May
4
comment Isomorphisms of rings and their generators
What does "when restricted to $x_1$" mean? You would have to extend $\phi$ in order for $\phi(x_1)$ to make sense.
May
4
answered Question: Graph Theory and Trees
May
4
answered System of equations solving for a b c d
May
4
comment How to find the number of real roots of the given equation?
Can you show that the left side is at most $2$, while the right side is at least $2$?
May
4
comment Isomorphisms of rings and their generators
One problem with $\phi(x_1)=x_1$ is that $x_1$ isn't in ${\bf Z}[x_1+x_2]$.
May
4
comment Is G isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$?
Find some generators of $G$; find some generators of the other group; see what happens when you map the one set to the other.
May
4
comment A basic question on factorization
Let $f(x)=x^2-2$, irreducible over the rationals; is $f(x/\sqrt2)$ irreducible?
May
4
revised A question about definition of hyperplane
edited tags