Question

functional equation on integers with divisibility: $f(a) + f(b)\mid 2(a + b - 1)$

score 93 · Answer 1 · 2026-04-15 20:34:42

93

Views

functional equation on integers with divisibility: $f(a) + f(b)\mid 2(a + b - 1)$

Published on 15 Apr 2026 - 20:34

score 38 · Answer 2 · 2026-04-10 23:24:01

38

Views

Function on integers satisfying two functional equation with values at a point + non-value at a point

Published on 10 Apr 2026 - 23:24

score 162 · Answer 3 · 2026-04-15 02:04:33

162

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How to obtain $f(x)$, if it is known that $f(f(x))=x^3+x$?

Published on 15 Apr 2026 - 2:04

score 840 · Answer 4 · 2026-04-16 03:28:29

840

Views

Find all function $f(n)$ satisfying $f(n)^2 = n f(f(n))$

Published on 16 Apr 2026 - 3:28

score 546 · Answer 5 · 2026-04-14 06:26:47

546

Views

Problems mainly based on a composite function $f(f(x))={f(x)}^3$

Published on 14 Apr 2026 - 6:26

score 109 · Answer 6 · 2026-04-09 06:14:19

109

Views

Functional equation with incommensurable periods

Published on 09 Apr 2026 - 6:14

score 83 · Answer 7 · 2026-04-11 21:41:35

83

Views

Reference for a mixed variational formulation of the heat equation

Published on 11 Apr 2026 - 21:41

score 170 · Answer 8 · 2026-04-15 17:55:06

170

Views

$f(f(x))=f(x),$ for all $x\in\Bbb R$ suppose $f$ is differentiable, show $f$ is constant or $f(x)=x$

Published on 15 Apr 2026 - 17:55

score 565 · Answer 9 · 2026-04-15 23:18:30

565

Views

If $f \circ f =f$, then what is $f$?

Published on 15 Apr 2026 - 23:18

score 38 · Answer 10 · 2026-04-15 13:47:48

38

Views

The function $f : R → R$ satisfies $x + f(x) = f(f(x))$ for every $x\in R$. Find all solutions of the equation $f(f(x)) = 0$.

Published on 15 Apr 2026 - 13:47

score 59 · Answer 11 · 2026-04-15 08:24:34

59

Views

Solution to $n+\alpha W\left(-e^{\frac{-n}{\alpha}} \right) \leq 1$ for $n$, where $n\geq \alpha >0$, all in the reals

Published on 15 Apr 2026 - 8:24

score 63 · Answer 12 · 2021-08-01 13:06:01

63

Views

If $f(x × f(y)) = \dfrac{f ( x) }y , x, y \in \mathbb R , y \ne 0$, then prove that $f(x) . f (1 /x) = 1$

Published on 01 Aug 2021 - 13:06

score 639 · Answer 13 · 2026-04-15 20:10:16

639

Views

If $f(xy) = e^{xy – x – y} (e^y f(x) + e^x f(y)) , x , y \in \mathbb R^+$ and $f ’ (1) = e$ , then find $f(x)$.

Published on 15 Apr 2026 - 20:10

score 367 · Answer 14 · 2026-04-08 22:21:31

367

Views

How to strengthen $ h \big( 2 h ( x ) \big) = h ( x ) + x $ to force $ h $ to be linear?

Published on 08 Apr 2026 - 22:21

score 108 · Answer 15 · 2026-04-12 10:49:27

108

Views

Is there an explicit solution to this equation?

Published on 12 Apr 2026 - 10:49

List Question

functional equation on integers with divisibility: $f(a) + f(b)\mid 2(a + b - 1)$

Function on integers satisfying two functional equation with values at a point + non-value at a point

How to obtain $f(x)$, if it is known that $f(f(x))=x^3+x$?

Find all function $f(n)$ satisfying $f(n)^2 = n f(f(n))$

Problems mainly based on a composite function $f(f(x))={f(x)}^3$

Functional equation with incommensurable periods

Reference for a mixed variational formulation of the heat equation

$f(f(x))=f(x),$ for all $x\in\Bbb R$ suppose $f$ is differentiable, show $f$ is constant or $f(x)=x$

If $f \circ f =f$, then what is $f$?

The function $f : R → R$ satisfies $x + f(x) = f(f(x))$ for every $x\in R$. Find all solutions of the equation $f(f(x)) = 0$.

Solution to $n+\alpha W\left(-e^{\frac{-n}{\alpha}} \right) \leq 1$ for $n$, where $n\geq \alpha >0$, all in the reals

If $f(x × f(y)) = \dfrac{f ( x) }y , x, y \in \mathbb R , y \ne 0$, then prove that $f(x) . f (1 /x) = 1$

If $f(xy) = e^{xy – x – y} (e^y f(x) + e^x f(y)) , x , y \in \mathbb R^+$ and $f ’ (1) = e$ , then find $f(x)$.

How to strengthen $ h \big( 2 h ( x ) \big) = h ( x ) + x $ to force $ h $ to be linear?

Is there an explicit solution to this equation?

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