Question

Take p an odd prime and $a$ an integer with order $d$ mod p, is it true that if $d$ is even, then $a^{\frac{d}{2}} \equiv -1\pmod p$

score 364 · Answer 1 · 2026-03-26 06:08:13

364

Views

Take p an odd prime and $a$ an integer with order $d$ mod p, is it true that if $d$ is even, then $a^{\frac{d}{2}} \equiv -1\pmod p$

Published on 26 Mar 2026 - 6:08

score 169 · Answer 2 · 2026-03-25 04:25:16

169

Views

Suppose $p$ is $3\bmod 4$. Show $a$ and $-a$ cannot both be primitive roots $\bmod p$.

Published on 25 Mar 2026 - 4:25

score 1.1k · Answer 3 · 2026-03-27 22:03:06

1.1k

Views

Inverse of a injective continuous map defined on a compact set is continuous.

Published on 27 Mar 2026 - 22:03

score 2k · Answer 4 · 2026-03-25 16:03:33

2k

Views

Show that the product of any $m$ consecutive positive integers is divisible by $m!$

Published on 25 Mar 2026 - 16:03

score 1.6k · Answer 5 · 2026-03-25 06:26:22

1.6k

Views

Showing continuity of a max function

Published on 25 Mar 2026 - 6:26

score 2.1k · Answer 6 · 2026-03-25 06:10:35

2.1k

Views

Compact operator can be approximated by finite rank operator

Published on 25 Mar 2026 - 6:10

score 97 · Answer 7 · 2018-04-08 03:54:57

97

Views

Show that if, for some $ψ$, $Γ \vdash ψ$ and $Γ \vdash ¬ψ$, then $Γ \vdash φ$, for any formula $φ$.

Published on 08 Apr 2018 - 3:54

score 292 · Answer 8 · 2026-03-25 17:24:39

292

Views

On a characterization of measure zero sets on $\mathbb{R}$ [Proof Verification]

Published on 25 Mar 2026 - 17:24

score 91 · Answer 9 · 2026-03-25 06:03:51

91

Views

Is the following an acceptable formal proof for $0! = 1$?

Published on 25 Mar 2026 - 6:03

score 688 · Answer 10 · 2026-03-25 01:33:02

688

Views

Well-defined, surjective map between two quotient spaces (Linear Algebra - beginner level)

Published on 25 Mar 2026 - 1:33

score 61 · Answer 11 · 2026-03-25 06:26:21

61

Views

Continuity and density with functions coinciding

Published on 25 Mar 2026 - 6:26

score 66 · Answer 12 · 2026-03-25 06:27:57

66

Views

Showing that $\lim_{x \to1} \log(x)= 0$

Published on 25 Mar 2026 - 6:27

score 228 · Answer 13 · 2026-03-29 21:22:43

228

Views

proof verification $\frac{3+2\sqrt{6}}{1-\sqrt{6}}$ is an algebraic integer

Published on 29 Mar 2026 - 21:22

score 51 · Answer 14 · 2018-04-08 16:26:28

51

Views

Prove/disprove: $f(x,y)=\{\{x\},\{y,\emptyset\}\}$ is an ordered pair map. (ZFC)

Published on 08 Apr 2018 - 16:26

score 315 · Answer 15 · 2026-03-29 17:00:18

315

Views

Suppose that $q: X\to Z$ and that $p: X\to Y$ are covering spaces. Suppose there is a continuous function $r: Y\to Z$ such that $r\circ p=q$.

Published on 29 Mar 2026 - 17:00

List Question

Take p an odd prime and $a$ an integer with order $d$ mod p, is it true that if $d$ is even, then $a^{\frac{d}{2}} \equiv -1\pmod p$

Suppose $p$ is $3\bmod 4$. Show $a$ and $-a$ cannot both be primitive roots $\bmod p$.

Inverse of a injective continuous map defined on a compact set is continuous.

Show that the product of any $m$ consecutive positive integers is divisible by $m!$

Showing continuity of a max function

Compact operator can be approximated by finite rank operator

Show that if, for some $ψ$, $Γ \vdash ψ$ and $Γ \vdash ¬ψ$, then $Γ \vdash φ$, for any formula $φ$.

On a characterization of measure zero sets on $\mathbb{R}$ [Proof Verification]

Is the following an acceptable formal proof for $0! = 1$?

Well-defined, surjective map between two quotient spaces (Linear Algebra - beginner level)

Continuity and density with functions coinciding

Showing that $\lim_{x \to1} \log(x)= 0$

proof verification $\frac{3+2\sqrt{6}}{1-\sqrt{6}}$ is an algebraic integer

Prove/disprove: $f(x,y)=\{\{x\},\{y,\emptyset\}\}$ is an ordered pair map. (ZFC)

Suppose that $q: X\to Z$ and that $p: X\to Y$ are covering spaces. Suppose there is a continuous function $r: Y\to Z$ such that $r\circ p=q$.

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