Question

Given a positive integer $n$, some straight lines and lattice points such... Prove that the number of the lines is at least $n(n+3)$.

score 405 · Answer 1 · 2026-03-26 02:57:43

405

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Given a positive integer $n$, some straight lines and lattice points such... Prove that the number of the lines is at least $n(n+3)$.

Published on 26 Mar 2026 - 2:57

score 170 · Answer 2 · 2026-04-15 12:44:35

170

Views

how to show $\frac{\cos (3(x - \frac{\pi}{4}))}{\cos(x - \frac{\pi}{4})} = \frac{\sin 3x - \cos 3x}{\sin x + \cos x}$

Published on 15 Apr 2026 - 12:44

score 112 · Answer 3 · 2026-04-15 12:50:23

112

Views

Proof of $|S \cup T| = |S| + |T| - |S \cap T|$

Published on 15 Apr 2026 - 12:50

score 155 · Answer 4 · 2026-04-15 12:42:03

155

Views

How to show $\cos^2A + \cos^2B = \frac{1}{2} \cos(2A + \frac{\pi}{3}) + 1$ more efficiently

Published on 15 Apr 2026 - 12:42

score 354 · Answer 5 · 2026-04-14 01:40:44

354

Views

Let $S$ a subspace and $V$ a vector space. Show that the additive identity of $S$ is the additive identity of $V$.

Published on 14 Apr 2026 - 1:40

score 591 · Answer 6 · 2026-04-15 12:42:27

591

Views

If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$

Published on 15 Apr 2026 - 12:42

score 187 · Answer 7 · 2026-04-09 15:08:32

187

Views

Natural deduction proof (Fitch) - Alternative using disjunction exclusion

Published on 09 Apr 2026 - 15:08

score 89 · Answer 8 · 2026-04-14 04:20:13

89

Views

Solving a specific linear parabolic PDE analytically

Published on 14 Apr 2026 - 4:20

score 119 · Answer 9 · 2026-04-15 12:51:13

119

Views

Solve the equation $10x^3-6x^2-12x-8=0$

Published on 15 Apr 2026 - 12:51

score 108 · Answer 10 · 2026-04-15 12:44:35

108

Views

$(x, y) \in$ $\mathbb{R} $, $x^2 +y^2 +xy=4$ and $x^4 +y^4 +(xy) ^2 =8$ calculate : $ x^6+(xy)^3+y^6$

Published on 15 Apr 2026 - 12:44

score 56 · Answer 11 · 2026-03-25 09:48:36

56

Views

Intermediate inequality for an inequality from Crux mathematicorum

Published on 25 Mar 2026 - 9:48

score 196 · Answer 12 · 2026-04-15 12:41:58

196

Views

Limit: Quotient of two functions

Published on 15 Apr 2026 - 12:41

score 131 · Answer 13 · 2026-03-26 23:11:46

131

Views

A cyclic inequality of degree 10

Published on 26 Mar 2026 - 23:11

score 80 · Answer 14 · 2026-04-12 05:01:51

80

Views

Combinatorial argument for identity with binomial coefficients

Published on 12 Apr 2026 - 5:01

score 36 · Answer 15 · 2026-04-15 12:39:14

36

Views

contrapositive and contradiction

Published on 15 Apr 2026 - 12:39

List Question

Given a positive integer $n$, some straight lines and lattice points such... Prove that the number of the lines is at least $n(n+3)$.

how to show $\frac{\cos (3(x - \frac{\pi}{4}))}{\cos(x - \frac{\pi}{4})} = \frac{\sin 3x - \cos 3x}{\sin x + \cos x}$

Proof of $|S \cup T| = |S| + |T| - |S \cap T|$

How to show $\cos^2A + \cos^2B = \frac{1}{2} \cos(2A + \frac{\pi}{3}) + 1$ more efficiently

Let $S$ a subspace and $V$ a vector space. Show that the additive identity of $S$ is the additive identity of $V$.

If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$

Natural deduction proof (Fitch) - Alternative using disjunction exclusion

Solving a specific linear parabolic PDE analytically

Solve the equation $10x^3-6x^2-12x-8=0$

$(x, y) \in$ $\mathbb{R} $, $x^2 +y^2 +xy=4$ and $x^4 +y^4 +(xy) ^2 =8$ calculate : $ x^6+(xy)^3+y^6$

Intermediate inequality for an inequality from Crux mathematicorum

Limit: Quotient of two functions

A cyclic inequality of degree 10

Combinatorial argument for identity with binomial coefficients

contrapositive and contradiction

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