Question

Functional equation in natural numbers with divisibility: $f(m) + f(n) + mn \ | \ m^2f(m) + n^2f(n) + f(m)f(n)$

score 290 · Answer 1 · 2026-04-16 14:45:56

290

Views

Functional equation in natural numbers with divisibility: $f(m) + f(n) + mn \ | \ m^2f(m) + n^2f(n) + f(m)f(n)$

Published on 16 Apr 2026 - 14:45

score 86 · Answer 2 · 2026-04-14 15:05:59

86

Views

How to solve this functional equation $f(xf(y))+y+f(x)=f(x+f(y))+yf(x)$?

Published on 14 Apr 2026 - 15:05

score 759 · Answer 3 · 2026-04-15 21:57:46

759

Views

Find all $f: \mathbb{R} \to \mathbb{R}$ such that $(f(x)+y)(f(x-y)+1)=f(f(xf(x+1))-yf(y-1)), \forall x,y \in \mathbb{R}$

Published on 15 Apr 2026 - 21:57

score 54 · Answer 4 · 2026-04-10 16:35:14

54

Views

Sum of roots of a functional equation

Published on 10 Apr 2026 - 16:35

score 39 · Answer 5 · 2026-04-16 19:47:33

39

Views

Maximising Property

Published on 16 Apr 2026 - 19:47

score 426 · Answer 6 · 2026-04-17 04:39:41

426

Views

Find all functions $f:\mathbb N\to \mathbb N$ such that $\frac{4f(x)f(y-3)}{f(x)f(y-2)+f(y)f(x-2)}$ is an integer for all $x>2$ and $y>3$.

Published on 17 Apr 2026 - 4:39

score 183 · Answer 7 · 2026-04-16 23:17:39

183

Views

Determine whether or not the function f it is bijective 2f(3-2x)+f(3/2-x/2)=x, where x is a real number

Published on 16 Apr 2026 - 23:17

score 140 · Answer 8 · 2026-04-15 10:35:38

140

Views

Q : Let $f : \mathbb Z\to \mathbb Z$ such that, for all $x,y\in\mathbb Z:$ $f(f(x) − y) = f(y) − f(f(x)).$ Show $f$ is bounded.

Published on 15 Apr 2026 - 10:35

score 161 · Answer 9 · 2026-04-17 13:52:35

161

Views

Find all functions $f:\mathbb{R}\to\mathbb{R}$ such as $x\left[f(x+y)-f(x-y)\right]=4yf(x)$

Published on 17 Apr 2026 - 13:52

score 111 · Answer 10 · 2026-04-17 12:04:09

111

Views

Find all functions s.t.$f(x^2-y^2)=xf(x)-yf(y)$

Published on 17 Apr 2026 - 12:04

score 85 · Answer 11 · 2026-04-16 08:22:27

85

Views

$f: \mathbb{N} \to \mathbb{N}$, Find $f$ with Mathematical Induction of the value of $f(x)-f(x-1).$

Published on 16 Apr 2026 - 8:22

score 76 · Answer 12 · 2026-04-16 16:44:05

How to go about finding a function that satisfies $f(x)=-f(x-1)^{2}+2^{2^{x-3}}f(x-1)+2^{2^{x-2}}$ (Or determining if such a function exists)

score 109 · Answer 13 · 2026-04-17 12:02:12

109

Views

$f:\mathbb{R} \to \mathbb{R}$ such that $f(x+y^2+f(y)) = f(x-y^2-f(y))$

Published on 17 Apr 2026 - 12:02

score 132 · Answer 14 · 2026-04-15 23:23:05

132

Views

Find closed form of $f(x)= \frac{1}{x} \sum_{i=1}^{k} f(x+i)$

Published on 15 Apr 2026 - 23:23

score 129 · Answer 15 · 2026-04-15 03:20:27

129

Views

Is my proof that $f(x)$ where $f(f(x)) = 6x - f(x)$ for all $f:R+→R+$ is linear correct?

Published on 15 Apr 2026 - 3:20

List Question

Functional equation in natural numbers with divisibility: $f(m) + f(n) + mn \ | \ m^2f(m) + n^2f(n) + f(m)f(n)$

How to solve this functional equation $f(xf(y))+y+f(x)=f(x+f(y))+yf(x)$?

Find all $f: \mathbb{R} \to \mathbb{R}$ such that $(f(x)+y)(f(x-y)+1)=f(f(xf(x+1))-yf(y-1)), \forall x,y \in \mathbb{R}$

Sum of roots of a functional equation

Maximising Property

Find all functions $f:\mathbb N\to \mathbb N$ such that $\frac{4f(x)f(y-3)}{f(x)f(y-2)+f(y)f(x-2)}$ is an integer for all $x>2$ and $y>3$.

Determine whether or not the function f it is bijective 2f(3-2x)+f(3/2-x/2)=x, where x is a real number

Q : Let $f : \mathbb Z\to \mathbb Z$ such that, for all $x,y\in\mathbb Z:$ $f(f(x) − y) = f(y) − f(f(x)).$ Show $f$ is bounded.

Find all functions $f:\mathbb{R}\to\mathbb{R}$ such as $x\left[f(x+y)-f(x-y)\right]=4yf(x)$

Find all functions s.t.$f(x^2-y^2)=xf(x)-yf(y)$

$f: \mathbb{N} \to \mathbb{N}$, Find $f$ with Mathematical Induction of the value of $f(x)-f(x-1).$

How to go about finding a function that satisfies $f(x)=-f(x-1)^{2}+2^{2^{x-3}}f(x-1)+2^{2^{x-2}}$ (Or determining if such a function exists)

$f:\mathbb{R} \to \mathbb{R}$ such that $f(x+y^2+f(y)) = f(x-y^2-f(y))$

Find closed form of $f(x)= \frac{1}{x} \sum_{i=1}^{k} f(x+i)$

Is my proof that $f(x)$ where $f(f(x)) = 6x - f(x)$ for all $f:R+→R+$ is linear correct?

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