Question

Can every binary functional equation be implemented algebraically in a pure way?

score 64 · Answer 1 · 2026-04-11 06:41:21

64

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Can every binary functional equation be implemented algebraically in a pure way?

Published on 11 Apr 2026 - 6:41

score 78 · Answer 2 · 2021-02-28 16:40:40

78

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functional equation $f\left(x\right)+a=f\left(x+b\right)$

Published on 28 Feb 2021 - 16:40

score 96 · Answer 3 · 2021-02-28 19:06:51

96

Views

Question to find all functions satisfying the functional equation $ f \left( f ( m ) ^ 2 + f ( n ) ^ 2 \right) = m ^ 2 + n ^ 2 $

Published on 28 Feb 2021 - 19:06

score 66 · Answer 4 · 2021-02-28 19:13:38

Question to find all strictly increasing $f:\mathbb{N}\to\mathbb{N}$ mapping only primes to primes and satisfying $f(2n)=f(n)+n$ for all $n$

score 193 · Answer 5 · 2021-03-01 15:51:22

193

Views

Find all functions satisfying $ f \left( m ^ 2 + f ( n ) \right) = f ( m ) ^ 2 + n $, for all $ m , n \in \mathbb N $

Published on 01 Mar 2021 - 15:51

score 83 · Answer 6 · 2021-03-02 03:26:00

83

Views

Solving functional equations including $f\circ f(x)$ functions

Published on 02 Mar 2021 - 3:26

score 133 · Answer 7 · 2021-03-02 13:55:43

133

Views

Finding $f$ such that $\forall x,y \in \mathbb{R},f(x+y)f(x-y)=(f(x))^2$

Published on 02 Mar 2021 - 13:55

score 44 · Answer 8 · 2026-04-08 12:32:10

44

Views

Sequences satisfying an identity involving a discrete convolution

Published on 08 Apr 2026 - 12:32

score 83 · Answer 9 · 2026-04-09 00:03:24

83

Views

Functional equation and normal distribution

Published on 09 Apr 2026 - 0:03

score 918 · Answer 10 · 2021-03-05 00:30:56

918

Views

Let $f:\mathbb{R} \to \mathbb{R}$ continuous with $f(f(x))=e^x$, show that $\lim_{x\to \infty } \frac{f(x)}{x^n}=\infty$ (Brazilian Olympiad)

Published on 05 Mar 2021 - 0:30

score 52 · Answer 11 · 2026-04-13 04:15:20

52

Views

Prove there is no function with the following property:

Published on 13 Apr 2026 - 4:15

score 81 · Answer 12 · 2026-04-04 02:21:32

81

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If $f(x)=1-f(x-a_1)f(x-a_2)...f(x-a_n)$, prove that $f$ is eventually periodic. (Czech and Slovak 2001)

Published on 04 Apr 2026 - 2:21

score 335 · Answer 13 · 2026-04-12 00:09:17

335

Views

Extremal of the variational problem $J[y] = \int_{0}^1 (y'(x))^2 dx$ with the conditions $y(0)=0$, $y(1) = 1$ and $\int_{0}^1 y(x)dx =0$

Published on 12 Apr 2026 - 0:09

score 201 · Answer 14 · 2021-03-16 13:11:50

201

Views

Determine all $f:\Bbb Z \to \Bbb Z$ st $f(x^3+y^3+z^3)=f(x)^3+f(y)^3+f(z)^3$. (Vietnamese TST 2005)

Published on 16 Mar 2021 - 13:11

score 283 · Answer 15 · 2021-03-19 10:56:18

283

Views

Non-linear bijections preserving the relation $fg = f^2$

Published on 19 Mar 2021 - 10:56

List Question

Can every binary functional equation be implemented algebraically in a pure way?

functional equation $f\left(x\right)+a=f\left(x+b\right)$

Question to find all functions satisfying the functional equation $ f \left( f ( m ) ^ 2 + f ( n ) ^ 2 \right) = m ^ 2 + n ^ 2 $

Question to find all strictly increasing $f:\mathbb{N}\to\mathbb{N}$ mapping only primes to primes and satisfying $f(2n)=f(n)+n$ for all $n$

Find all functions satisfying $ f \left( m ^ 2 + f ( n ) \right) = f ( m ) ^ 2 + n $, for all $ m , n \in \mathbb N $

Solving functional equations including $f\circ f(x)$ functions

Finding $f$ such that $\forall x,y \in \mathbb{R},f(x+y)f(x-y)=(f(x))^2$

Sequences satisfying an identity involving a discrete convolution

Functional equation and normal distribution

Let $f:\mathbb{R} \to \mathbb{R}$ continuous with $f(f(x))=e^x$, show that $\lim_{x\to \infty } \frac{f(x)}{x^n}=\infty$ (Brazilian Olympiad)

Prove there is no function with the following property:

If $f(x)=1-f(x-a_1)f(x-a_2)...f(x-a_n)$, prove that $f$ is eventually periodic. (Czech and Slovak 2001)

Extremal of the variational problem $J[y] = \int_{0}^1 (y'(x))^2 dx$ with the conditions $y(0)=0$, $y(1) = 1$ and $\int_{0}^1 y(x)dx =0$

Determine all $f:\Bbb Z \to \Bbb Z$ st $f(x^3+y^3+z^3)=f(x)^3+f(y)^3+f(z)^3$. (Vietnamese TST 2005)

Non-linear bijections preserving the relation $fg = f^2$

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