Question

Number of solutions to $a-b^2\ge\frac 14, b-c^2\ge\frac 14, c-d^2\ge\frac 14, d-a^2\ge\frac 14$

score 177 · Answer 1 · 2026-04-17 14:27:01

177

Views

Number of solutions to $a-b^2\ge\frac 14, b-c^2\ge\frac 14, c-d^2\ge\frac 14, d-a^2\ge\frac 14$

Published on 17 Apr 2026 - 14:27

score 91 · Answer 2 · 2026-04-14 02:45:37

91

Views

Result comparison of a trigonometric equation

Published on 14 Apr 2026 - 2:45

score 21 · Answer 3 · 2026-04-11 10:47:12

21

Views

Factorisation involving four terms (grouping two and two)

Published on 11 Apr 2026 - 10:47

score 63 · Answer 4 · 2026-04-16 22:56:29

63

Views

Showing $x-a>y-b$ implies $\frac{x}{y}>\frac{b}{a}$ and $x>y$?

Published on 16 Apr 2026 - 22:56

score 115 · Answer 5 · 2026-04-11 19:28:28

115

Views

Finding minimum possible value of $n+z^3$

Published on 11 Apr 2026 - 19:28

score 844 · Answer 6 · 2026-04-13 19:54:31

844

Views

How to solve the problem "A large room contains two speakers that are 3 meters apart …"?

Published on 13 Apr 2026 - 19:54

score 62 · Answer 7 · 2026-04-15 10:44:03

62

Views

Rings in which the "mistake" $(x + y) / d = x / d + y$ is justified

Published on 15 Apr 2026 - 10:44

score 62 · Answer 8 · 2026-04-13 19:35:46

62

Views

$\cot x - \tan x = 2\cot 2x$, but the period on the left is $\pi$, while on the right it's $\pi/2$. Shouldn't the periods match?

Published on 13 Apr 2026 - 19:35

score 553 · Answer 9 · 2026-04-14 17:00:31

553

Views

British Maths Olympiad (BMO) 2004 Round 1 Question 3 Proof with pigeon hole principle?

Published on 14 Apr 2026 - 17:00

score 99 · Answer 10 · 2026-04-24 02:02:54

99

Views

Is $\cos(x+y)=e^x$ an implicit function?

Published on 24 Apr 2026 - 2:02

score 35 · Answer 11 · 2026-04-16 13:16:30

35

Views

Finding an appropriate upper bound for $\frac{x^2-4}{x-1}$ at $x=0$ and $x=2$

Published on 16 Apr 2026 - 13:16

score 129 · Answer 12 · 2026-04-12 11:57:35

129

Views

Which $z\in\mathbb{C}$ satisfy the equation $|z-i|=\sqrt{2}|\bar{z}+1|$?

Published on 12 Apr 2026 - 11:57

score 46 · Answer 13 · 2026-04-11 20:50:46

46

Views

log rules for MLE

Published on 11 Apr 2026 - 20:50

score 2.8k · Answer 14 · 2026-04-20 11:28:41

2.8k

Views

If $|z| < 1$, prove that $\Re \left(\frac{1}{1 - z} \right) > \frac{1}{2}$.

Published on 20 Apr 2026 - 11:28

score 5k · Answer 15 · 2026-04-15 08:31:52

5k

Views

Intuition for why the difference between $\frac{2x^2-x}{x^2-x+1}$ and $\frac{x-2}{x^2-x+1}$ is a constant?

Published on 15 Apr 2026 - 8:31

List Question

Number of solutions to $a-b^2\ge\frac 14, b-c^2\ge\frac 14, c-d^2\ge\frac 14, d-a^2\ge\frac 14$

Result comparison of a trigonometric equation

Factorisation involving four terms (grouping two and two)

Showing $x-a>y-b$ implies $\frac{x}{y}>\frac{b}{a}$ and $x>y$?

Finding minimum possible value of $n+z^3$

How to solve the problem "A large room contains two speakers that are 3 meters apart …"?

Rings in which the "mistake" $(x + y) / d = x / d + y$ is justified

$\cot x - \tan x = 2\cot 2x$, but the period on the left is $\pi$, while on the right it's $\pi/2$. Shouldn't the periods match?

British Maths Olympiad (BMO) 2004 Round 1 Question 3 Proof with pigeon hole principle?

Is $\cos(x+y)=e^x$ an implicit function?

Finding an appropriate upper bound for $\frac{x^2-4}{x-1}$ at $x=0$ and $x=2$

Which $z\in\mathbb{C}$ satisfy the equation $|z-i|=\sqrt{2}|\bar{z}+1|$?

log rules for MLE

If $|z| < 1$, prove that $\Re \left(\frac{1}{1 - z} \right) > \frac{1}{2}$.

Intuition for why the difference between $\frac{2x^2-x}{x^2-x+1}$ and $\frac{x-2}{x^2-x+1}$ is a constant?

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