Question

Solutions to the functional equation $f(f(x))=f(x+1)$

score 123 · Answer 1 · 2026-04-17 13:58:50

123

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Solutions to the functional equation $f(f(x))=f(x+1)$

Published on 17 Apr 2026 - 13:58

score 268 · Answer 2 · 2026-04-15 09:41:51

268

Views

Let n be a positive integer. Find the number of positive integers whose base n representation has some other properties (USAMO 1990)

Published on 15 Apr 2026 - 9:41

score 268 · Answer 3 · 2026-04-16 09:47:42

268

Views

A $\Delta ABC$ has vertices lying on a circle $w$ of radius $1$, with $\angle BAC = 60^\circ$. A circle with center $I$ is inscribed in $\Delta ABC$.

Published on 16 Apr 2026 - 9:47

score 69 · Answer 4 · 2026-04-15 19:39:29

69

Views

Solve in $\mathbb{R}$ the equation $3x+\sqrt[3]{x+1}+\sqrt[3]{(x+1)^2}=-1$

Published on 15 Apr 2026 - 19:39

score 162 · Answer 5 · 2026-04-15 20:18:24

162

Views

In $\mathbb{R}$ find the solutions of the equation $x^4-x^3-18x^2+3x+9=0$

Published on 15 Apr 2026 - 20:18

score 452 · Answer 6 · 2026-03-25 17:42:05

452

Views

In $\Delta ABC$, $AB = 14, BC = 16, AC = 26$. $M$ is the midpoint of $BC$ and $D$ is the point on $BC$ such that $AD$ bisects $\angle BAC$.

Published on 25 Mar 2026 - 17:42

score 31 · Answer 7 · 2026-04-15 02:53:59

31

Views

Let $P$ be a point on $DE$ and let the extensions of $BP$ and $CP$ meet the sides $AC$ and $AB$ at $G$ and $F$ respectively.

Published on 15 Apr 2026 - 2:53

score 508 · Answer 8 · 2026-04-13 21:22:36

508

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In $\Delta ABC$ , $\angle A = 20^\circ, \angle C = 90^\circ$. $O$ is a point on $AB$ and $D$ is the midpoint of $OB$ . Find $\angle BCD$ .

Published on 13 Apr 2026 - 21:22

score 762 · Answer 9 · 2026-04-14 23:15:27

762

Views

In $\Delta ABC , D$ and $E$ are midpoints of the sides $AB$ and $AC$ respectively, $CD$ and $BE$ intersect at $P$ with $\angle BPC = 90^\circ$.

Published on 14 Apr 2026 - 23:15

score 375 · Answer 10 · 2026-04-14 16:07:28

375

Views

In $\Delta ABC$ where $\angle A = 60^\circ$, $BP$ and $BE$ trisect $\angle ABC$ and $CP$ and $CE$ trisect $\angle ACB$ . Find $\angle BPE$ .

Published on 14 Apr 2026 - 16:07

score 484 · Answer 11 · 2026-04-11 23:11:11

484

Views

Intuitive Understanding of exponential distrbution

Published on 11 Apr 2026 - 23:11

score 469 · Answer 12 · 2026-04-13 13:07:56

469

Views

A stick of fixed length is broken into 3 pieces. Construct triangle

Published on 13 Apr 2026 - 13:07

score 484 · Answer 13 · 2026-04-15 07:35:05

484

Views

In $\Delta ABC, AB = AC = \sqrt{3}$ and $D$ is a point on $BC$ such that $AD = 1$ . Find $(BD\times DC)$ .

Published on 15 Apr 2026 - 7:35

score 1k · Answer 14 · 2026-04-16 13:58:00

1k

Views

Point $M$ lies inside $\triangle ABC$, $\angle MAC = 10^\circ$ and $\angle MCA = 30^\circ$. Find $(180^\circ - \angle BMC)$

Published on 16 Apr 2026 - 13:58

score 63 · Answer 15 · 2026-04-14 19:47:31

63

Views

Let $D$ and $E$ be points on $AB$ and $BC$ of $\Delta ABC$ such that $AD = 7BD$ , $BE = 10CE$ . Let $AE$ and $BC$ meet at point $F$

Published on 14 Apr 2026 - 19:47

List Question

Solutions to the functional equation $f(f(x))=f(x+1)$

Let n be a positive integer. Find the number of positive integers whose base n representation has some other properties (USAMO 1990)

A $\Delta ABC$ has vertices lying on a circle $w$ of radius $1$, with $\angle BAC = 60^\circ$. A circle with center $I$ is inscribed in $\Delta ABC$.

Solve in $\mathbb{R}$ the equation $3x+\sqrt[3]{x+1}+\sqrt[3]{(x+1)^2}=-1$

In $\mathbb{R}$ find the solutions of the equation $x^4-x^3-18x^2+3x+9=0$

In $\Delta ABC$, $AB = 14, BC = 16, AC = 26$. $M$ is the midpoint of $BC$ and $D$ is the point on $BC$ such that $AD$ bisects $\angle BAC$.

Let $P$ be a point on $DE$ and let the extensions of $BP$ and $CP$ meet the sides $AC$ and $AB$ at $G$ and $F$ respectively.

In $\Delta ABC$ , $\angle A = 20^\circ, \angle C = 90^\circ$. $O$ is a point on $AB$ and $D$ is the midpoint of $OB$ . Find $\angle BCD$ .

In $\Delta ABC , D$ and $E$ are midpoints of the sides $AB$ and $AC$ respectively, $CD$ and $BE$ intersect at $P$ with $\angle BPC = 90^\circ$.

In $\Delta ABC$ where $\angle A = 60^\circ$, $BP$ and $BE$ trisect $\angle ABC$ and $CP$ and $CE$ trisect $\angle ACB$ . Find $\angle BPE$ .

Intuitive Understanding of exponential distrbution

A stick of fixed length is broken into 3 pieces. Construct triangle

In $\Delta ABC, AB = AC = \sqrt{3}$ and $D$ is a point on $BC$ such that $AD = 1$ . Find $(BD\times DC)$ .

Point $M$ lies inside $\triangle ABC$, $\angle MAC = 10^\circ$ and $\angle MCA = 30^\circ$. Find $(180^\circ - \angle BMC)$

Let $D$ and $E$ be points on $AB$ and $BC$ of $\Delta ABC$ such that $AD = 7BD$ , $BE = 10CE$ . Let $AE$ and $BC$ meet at point $F$

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