Question

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

score 403 · Answer 1 · 2026-04-12 08:35:12

403

Views

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

Published on 12 Apr 2026 - 8:35

score 114 · Answer 2 · 2026-04-12 19:58:38

114

Views

Determining whether or not a relation involving absolute value is transitive

Published on 12 Apr 2026 - 19:58

score 1.7k · Answer 3 · 2026-04-11 17:43:50

1.7k

Views

Axiom of Choice implies Well-Ordering Principle

Published on 11 Apr 2026 - 17:43

score 145 · Answer 4 · 2026-04-15 09:17:16

145

Views

Solution verification: evaluate $\lim\limits_{n \to \infty}\frac{1^{\lambda n}+2^{\lambda n}+\cdots+n^{\lambda n}}{n^{\lambda n}}$ where $\lambda>0.$

Published on 15 Apr 2026 - 9:17

score 80 · Answer 5 · 2026-04-15 02:50:30

Let $a<b<c$, where $a$ is a positive integer and $b$ and $c$ are odd primes. Prove that if $a \mid (3b+2c)$ and $a \mid (2b+3c)$, then $a=1$ or $5$.

score 955 · Answer 6 · 2026-04-15 05:46:43

955

Views

Well-Ordering Principle implies Zorn's Lemma

Published on 15 Apr 2026 - 5:46

score 325 · Answer 7 · 2026-04-11 19:27:51

325

Views

Zorn's Lemma implies Axiom of Choice

Published on 11 Apr 2026 - 19:27

score 54 · Answer 8 · 2026-04-15 17:55:15

54

Views

If $(A,\preccurlyeq)$ is a linear ordering such that $|\{y\in A\mid y\preccurlyeq x\}| < \aleph_\gamma$ for all $x\in A$, then $|A|\le\aleph_\gamma$

Published on 15 Apr 2026 - 17:55

score 39 · Answer 9 · 2026-04-14 04:28:31

39

Views

Am I right in this proof of a criterion for the nonsingularity of a conic curve?

Published on 14 Apr 2026 - 4:28

score 85 · Answer 10 · 2026-04-10 19:35:54

85

Views

Union of closures

Published on 10 Apr 2026 - 19:35

score 164 · Answer 11 · 2026-04-16 21:46:28

164

Views

$a < b$ and $c<d$ imply $a+c < b+d$

Published on 16 Apr 2026 - 21:46

score 26 · Answer 12 · 2026-04-15 15:03:34

26

Views

Prove derivative of order $n$ at neighbourhood $x_0$

Published on 15 Apr 2026 - 15:03

score 55 · Answer 13 · 2026-04-15 23:17:04

55

Views

$a = d$ implies $a^b = d^b$

Published on 15 Apr 2026 - 23:17

score 7.6k · Answer 14 · 2026-04-12 00:43:31

7.6k

Views

Prove that if $A^2=0$, then $0$ is the only eigenvalue of $A$.

Published on 12 Apr 2026 - 0:43

score 221 · Answer 15 · 2026-04-15 05:03:25

221

Views

A closed (?) subset of the set of probability measures. Is my reasoning correct?

Published on 15 Apr 2026 - 5:03

List Question

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

Determining whether or not a relation involving absolute value is transitive

Axiom of Choice implies Well-Ordering Principle

Solution verification: evaluate $\lim\limits_{n \to \infty}\frac{1^{\lambda n}+2^{\lambda n}+\cdots+n^{\lambda n}}{n^{\lambda n}}$ where $\lambda>0.$

Let $a<b<c$, where $a$ is a positive integer and $b$ and $c$ are odd primes. Prove that if $a \mid (3b+2c)$ and $a \mid (2b+3c)$, then $a=1$ or $5$.

Well-Ordering Principle implies Zorn's Lemma

Zorn's Lemma implies Axiom of Choice

If $(A,\preccurlyeq)$ is a linear ordering such that $|\{y\in A\mid y\preccurlyeq x\}| < \aleph_\gamma$ for all $x\in A$, then $|A|\le\aleph_\gamma$

Am I right in this proof of a criterion for the nonsingularity of a conic curve?

Union of closures

$a < b$ and $c<d$ imply $a+c < b+d$

Prove derivative of order $n$ at neighbourhood $x_0$

$a = d$ implies $a^b = d^b$

Prove that if $A^2=0$, then $0$ is the only eigenvalue of $A$.

A closed (?) subset of the set of probability measures. Is my reasoning correct?

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