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An elegant proof for this simple graph problem

score 78 · Answer 1 · 2026-04-13 06:15:47

78

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An elegant proof for this simple graph problem

Published on 13 Apr 2026 - 6:15

score 254 · Answer 2 · 2026-04-14 11:43:03

254

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Solving the system $\tan x+\sin y+\sin z=3x$, $\sin x+\tan y+\sin z=3y$, $\sin x+\sin y+\tan z=3z$

Published on 14 Apr 2026 - 11:43

score 64 · Answer 3 · 2026-04-12 08:32:03

64

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A proof for If $a>0$ AND $r<s$ then: $a>1⇔a^r<a^s$ without using the natural logarithm function?

Published on 12 Apr 2026 - 8:32

score 729 · Answer 4 · 2026-03-25 13:56:20

729

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Inscribing Platonic solids in each other: why can't you put a dodecahedron in an octahedron?

Published on 25 Mar 2026 - 13:56

score 79 · Answer 5 · 2026-04-08 20:36:58

79

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Alternate proof of integral equality using MVT

Published on 08 Apr 2026 - 20:36

score 30 · Answer 6 · 2026-04-16 07:43:41

30

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Prove ${x \choose k}1/x^k < {y \choose k}1/y^k$ given that $x < y$ and $x, y \in \mathbb{N}$

Published on 16 Apr 2026 - 7:43

score 49 · Answer 7 · 2026-04-17 03:32:48

49

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Matrix $A$ can be written as a linear combination of $n \times n$ matrices with all the entries zero except one of them which is one.

Published on 17 Apr 2026 - 3:32

score 303 · Answer 8 · 2026-04-13 02:36:09

303

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How do I reason with Skolem functions?

Published on 13 Apr 2026 - 2:36

score 122 · Answer 9 · 2026-03-25 23:22:52

122

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prove $\sum_\text{cyc}\frac{a+2}{b+2}\le \sum_\text{cyc}\frac{a}{b}$

Published on 25 Mar 2026 - 23:22

score 522 · Answer 10 · 2026-04-15 09:07:02

522

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Find a winning strategy in a stone game.

Published on 15 Apr 2026 - 9:07

score 229 · Answer 11 · 2026-04-15 05:35:23

229

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Deriving AM-GM in a way that reflects my intuition.

Published on 15 Apr 2026 - 5:35

score 71 · Answer 12 · 2026-04-16 21:47:17

71

Views

Let $n \ge 3$. For $[a] \in (\Bbb Z /{2^n} \Bbb Z)^\times$ the relation $x^2 \equiv a \pmod {2^n}$ has either $0$ or $4$ residue solutions.

Published on 16 Apr 2026 - 21:47

score 67 · Answer 13 · 2026-04-10 17:44:59

67

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Equation of line through two tangents of the circle

Published on 10 Apr 2026 - 17:44

score 473 · Answer 14 · 2026-04-13 03:37:21

473

Views

Greatest coefficient of $x$ in expansion of $(1+2x)^8$

Published on 13 Apr 2026 - 3:37

score 278 · Answer 15 · 2026-04-14 09:35:52

278

Views

Can the Stolz-Cesàro theorem be used to prove L'Hospital's rule, or viceversa?

Published on 14 Apr 2026 - 9:35

List Question

An elegant proof for this simple graph problem

Solving the system $\tan x+\sin y+\sin z=3x$, $\sin x+\tan y+\sin z=3y$, $\sin x+\sin y+\tan z=3z$

A proof for If $a>0$ AND $r<s$ then: $a>1⇔a^r<a^s$ without using the natural logarithm function?

Inscribing Platonic solids in each other: why can't you put a dodecahedron in an octahedron?

Alternate proof of integral equality using MVT

Prove ${x \choose k}1/x^k < {y \choose k}1/y^k$ given that $x < y$ and $x, y \in \mathbb{N}$

Matrix $A$ can be written as a linear combination of $n \times n$ matrices with all the entries zero except one of them which is one.

How do I reason with Skolem functions?

prove $\sum_\text{cyc}\frac{a+2}{b+2}\le \sum_\text{cyc}\frac{a}{b}$

Find a winning strategy in a stone game.

Deriving AM-GM in a way that reflects my intuition.

Let $n \ge 3$. For $[a] \in (\Bbb Z /{2^n} \Bbb Z)^\times$ the relation $x^2 \equiv a \pmod {2^n}$ has either $0$ or $4$ residue solutions.

Equation of line through two tangents of the circle

Greatest coefficient of $x$ in expansion of $(1+2x)^8$

Can the Stolz-Cesàro theorem be used to prove L'Hospital's rule, or viceversa?

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