Question

Given a three digit number $n$, let $f(n)$ be the sum of digits of $n$, their products in pairs, and the product of all digits. When does $n=f(n)$?

score 1.2k · Answer 1 · 2018-11-19 05:36:37

Given a three digit number $n$, let $f(n)$ be the sum of digits of $n$, their products in pairs, and the product of all digits. When does $n=f(n)$?

score 198 · Answer 2 · 2018-11-19 05:46:29

198

Views

Proving that there is an element common to all $35$ sets given certain set restrictions

Published on 19 Nov 2018 - 5:46

score 78 · Answer 3 · 2026-03-25 03:07:34

78

Views

Prove that the polynomial is $g(x,y)(x^2 + y^2 -1)^2 + c$

Published on 25 Mar 2026 - 3:07

score 95 · Answer 4 · 2026-03-27 16:03:55

95

Views

Cover the plane with closed disks

Published on 27 Mar 2026 - 16:03

score 170 · Answer 5 · 2018-11-21 02:39:00

170

Views

Prove that $f(n)\ge 2^{n-1}$

Published on 21 Nov 2018 - 2:39

score 188 · Answer 6 · 2018-11-21 12:05:52

188

Views

$x_n = \left[1^{1^p}2^{2^p}\cdots (n+1)^{(n+1)^p}\right]-\left[1^{1^p}2^{2^p}\cdots n^{n^p}\right]$ converge?

Published on 21 Nov 2018 - 12:05

score 948 · Answer 7 · 2018-11-21 13:18:21

948

Views

Number of increasing sequences alternating between odd and even involving only integers from the set $[1, 2, 3, ..., n]$

Published on 21 Nov 2018 - 13:18

score 282 · Answer 8 · 2018-11-22 06:04:29

282

Views

Circular Geometry

Published on 22 Nov 2018 - 6:04

score 144 · Answer 9 · 2026-03-25 10:56:00

144

Views

Expected profit of my simple board game

Published on 25 Mar 2026 - 10:56

score 126 · Answer 10 · 2018-11-23 06:22:48

126

Views

$\sum_{i=1}^{\infty}\frac{1}{a_i}$ converges.,prove that $\lim_{n \to \infty}\frac{b_n}{n}=0$.

Published on 23 Nov 2018 - 6:22

score 86 · Answer 11 · 2018-11-23 08:01:40

86

Views

An inequality to finalize a proof

Published on 23 Nov 2018 - 8:01

score 108 · Answer 12 · 2018-11-23 19:20:20

108

Views

Find all real numbers $x,y,z\in [0,1]^3$ such that $(x^2+y^2)\sqrt{1-z^2}\ge z$....

Published on 23 Nov 2018 - 19:20

score 522 · Answer 13 · 2018-11-23 21:54:20

522

Views

Alternative proof that if $a,b,c \in \mathbb{R}$ and $(a+b+c)c<0$ then $b^2-4ac>0$?

Published on 23 Nov 2018 - 21:54

score 4.5k · Answer 14 · 2018-11-26 01:59:24

4.5k

Views

Prove that there exists a triangle which can be cut into 2005 congruent triangles.

Published on 26 Nov 2018 - 1:59

score 117 · Answer 15 · 2018-11-26 02:52:18

117

Views

Don't know where to use the hypothesis

Published on 26 Nov 2018 - 2:52

List Question

Given a three digit number $n$, let $f(n)$ be the sum of digits of $n$, their products in pairs, and the product of all digits. When does $n=f(n)$?

Proving that there is an element common to all $35$ sets given certain set restrictions

Prove that the polynomial is $g(x,y)(x^2 + y^2 -1)^2 + c$

Cover the plane with closed disks

Prove that $f(n)\ge 2^{n-1}$

$x_n = \left[1^{1^p}2^{2^p}\cdots (n+1)^{(n+1)^p}\right]-\left[1^{1^p}2^{2^p}\cdots n^{n^p}\right]$ converge?

Number of increasing sequences alternating between odd and even involving only integers from the set $[1, 2, 3, ..., n]$

Circular Geometry

Expected profit of my simple board game

$\sum_{i=1}^{\infty}\frac{1}{a_i}$ converges.,prove that $\lim_{n \to \infty}\frac{b_n}{n}=0$.

An inequality to finalize a proof

Find all real numbers $x,y,z\in [0,1]^3$ such that $(x^2+y^2)\sqrt{1-z^2}\ge z$....

Alternative proof that if $a,b,c \in \mathbb{R}$ and $(a+b+c)c<0$ then $b^2-4ac>0$?

Prove that there exists a triangle which can be cut into 2005 congruent triangles.

Don't know where to use the hypothesis

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