Sanchez

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I really appreciate it when you take time to answer my questions. Thanks!


102 Answers

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11
When is $(p - 1)! + 1$ a power of $p$?
10
Prove that for any $x \in \mathbb N$ such that $x<n!$ is the sum of at most $n$ distinct divisors of $n!$
10
Find three polynomials whose squares sum up to $x^4 + y^4 + x^2 + y^2$
8
Given $a+b+c=0$, simplify the following.
7
Can you provide me historical examples of pure mathematics becoming “useful”?
7
Irreducible Representations
6
Prove that $ \left(1+\frac a b \right) \left(1+\frac b c \right)\left(1+\frac c a \right) \geq 2\left(1+ \frac{a+b+c}{\sqrt[3]{abc}}\right)$.
6
Exterior Algebra as quotient
6
Let $a_{i} \in\mathbb{R}$ ($i=1,2,\dots,n$), and $f(x)=\sum_{i=0}^{n}a_{i}x^i$ such that if $|x|\leqslant 1$, then $|f(x)|\leqslant 1$. Prove that:
6
Prove that $\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}\geq\frac{1}{2}(a+b+c)$ for positive $a,b,c$
6
Basic trace inequality
5
A question about prime ideals
5
Tangent Space Exercise
5
Hartshorne Lemma I.6.5; Why is $\mathfrak{m}_R\cap B\neq 0$?
5
$\dfrac{(b+c-a)^2}{(b+c)^2+a^2}+ \frac{(c+a-b)^2}{(c+a)^2+b^2}+ \frac{(a+b-c)^2}{(a+b)^2+c^2} \ge \frac{3}{5}$
5
Ask for hint of an inequality
4
Intersection of open affines can be covered by open sets distinguished in *both*affines
4
Special Case of Lying Over Theorem
4
Intersection of a closed subscheme and an open subscheme of a scheme
4
Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
4
$\mathrm{Spec}(R)\!=\!\mathrm{Max}(R)\!\cup\!\{0\}$ $\Rightarrow$ $R$ is a PID
4
Is the radical of a homogeneous ideal of a graded ring homogeneous?
4
simple set theoretic question of subsets of $\mathbb R^d$
3
Planes, quadric surfaces and then …?
3
Prove That $x=y=z$
3
Given one inequality, prove second inequality
3
The image of the diagonal map in scheme
3
Definition of nebentypus in $L$-functions.
3
How prove this $(abc)^4+abc(a^3c^2+b^3a^2+c^3b^2)\le 4$
3
Formal finite sum for integration on k-chains
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