Question

If $f : \mathbb{N} \to \mathbb{N}$ and $f(x)=f(2x^2)$ find all possible solutions

score 66 · Answer 1 · 2018-05-31 03:21:52

66

Views

If $f : \mathbb{N} \to \mathbb{N}$ and $f(x)=f(2x^2)$ find all possible solutions

Published on 31 May 2018 - 3:21

score 641 · Answer 2 · 2018-05-31 12:19:57

641

Views

Finding all differentiable $f: [0,+\infty) \rightarrow [0,+\infty)$ such that $f(x) = f'(x^2)$ and $f(0)=0$

Published on 31 May 2018 - 12:19

score 76 · Answer 3 · 2018-05-31 13:45:57

76

Views

Unsymmetric Functional equations

Published on 31 May 2018 - 13:45

score 89 · Answer 4 · 2018-05-31 13:53:01

89

Views

Number of Functions satisfying linear homogeneous function criterion

Published on 31 May 2018 - 13:53

score 225 · Answer 5 · 2018-06-01 22:54:40

225

Views

Solving $f\left(x\right)+f\left(1/x\right)=K$

Published on 01 Jun 2018 - 22:54

score 302 · Answer 6 · 2018-06-02 03:09:18

Finding all functions $ f : \mathbb R \to \mathbb R $ satisfying $ f ( x ) f ( y ) + f ( x y ) + f ( x ) + f ( y ) = f ( x + y ) + 2 x y $

score 166 · Answer 7 · 2018-06-04 08:48:21

166

Views

$f(x-y)=f(x)f(y)$

Published on 04 Jun 2018 - 8:48

score 518 · Answer 8 · 2018-06-04 19:04:27

518

Views

How to solve $\dot x(t) = x(2t)$

Published on 04 Jun 2018 - 19:04

score 82 · Answer 9 · 2018-06-06 16:11:16

82

Views

Find all pairs of functions such that $f(x) +g(y) = x^2y^2$

Published on 06 Jun 2018 - 16:11

score 113 · Answer 10 · 2018-06-07 18:37:13

113

Views

Solution of the functional equation $f(x) + f(y) =f\left(x\sqrt{1-y^2 }+y\sqrt{1-x^2 }\right) $

Published on 07 Jun 2018 - 18:37

score 104 · Answer 11 · 2018-06-09 16:20:48

104

Views

Finding $f(x)$ from the functional equation $(e^x-1)f(2x)= \left(e^{2x}-1\right)f(x)$ and $f'(0) =1 $

Published on 09 Jun 2018 - 16:20

score 94 · Answer 12 · 2018-06-10 11:03:52

94

Views

Prove that there do not exist distinct integers $a,b,c$ and polynomial $P$, with integer coefficients, such that $P(a)=b, P(b)=c, P(c)=a$.

Published on 10 Jun 2018 - 11:03

score 79 · Answer 13 · 2018-06-10 17:31:10

79

Views

System of functional equations

Published on 10 Jun 2018 - 17:31

score 76 · Answer 14 · 2018-06-12 14:18:20

76

Views

Can this fuctional equation be solved?

Published on 12 Jun 2018 - 14:18

score 136 · Answer 15 · 2026-03-25 01:19:05

136

Views

Functional Square Root of Digit Sum?

Published on 25 Mar 2026 - 1:19

List Question

If $f : \mathbb{N} \to \mathbb{N}$ and $f(x)=f(2x^2)$ find all possible solutions

Finding all differentiable $f: [0,+\infty) \rightarrow [0,+\infty)$ such that $f(x) = f'(x^2)$ and $f(0)=0$

Unsymmetric Functional equations

Number of Functions satisfying linear homogeneous function criterion

Solving $f\left(x\right)+f\left(1/x\right)=K$

Finding all functions $ f : \mathbb R \to \mathbb R $ satisfying $ f ( x ) f ( y ) + f ( x y ) + f ( x ) + f ( y ) = f ( x + y ) + 2 x y $

$f(x-y)=f(x)f(y)$

How to solve $\dot x(t) = x(2t)$

Find all pairs of functions such that $f(x) +g(y) = x^2y^2$

Solution of the functional equation $f(x) + f(y) =f\left(x\sqrt{1-y^2 }+y\sqrt{1-x^2 }\right) $

Finding $f(x)$ from the functional equation $(e^x-1)f(2x)= \left(e^{2x}-1\right)f(x)$ and $f'(0) =1 $

Prove that there do not exist distinct integers $a,b,c$ and polynomial $P$, with integer coefficients, such that $P(a)=b, P(b)=c, P(c)=a$.

System of functional equations

Can this fuctional equation be solved?

Functional Square Root of Digit Sum?

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