Question

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

score 69 · Answer 1 · 2026-04-15 04:17:59

69

Views

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

Published on 15 Apr 2026 - 4:17

score 644 · Answer 2 · 2026-04-16 04:42:43

644

Views

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

Published on 16 Apr 2026 - 4:42

score 79 · Answer 3 · 2026-04-10 17:23:05

79

Views

Unsymmetric Functional equations

Published on 10 Apr 2026 - 17:23

score 92 · Answer 4 · 2026-04-15 19:33:07

92

Views

Number of Functions satisfying linear homogeneous function criterion

Published on 15 Apr 2026 - 19:33

score 228 · Answer 5 · 2026-04-17 08:21:26

228

Views

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

Published on 17 Apr 2026 - 8:21

score 305 · Answer 6 · 2026-04-15 23:35:52

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 170 · Answer 7 · 2026-05-10 21:23:27

170

Views

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

Published on 10 May 2026 - 21:23

score 521 · Answer 8 · 2026-04-14 17:55:39

521

Views

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

Published on 14 Apr 2026 - 17:55

score 85 · Answer 9 · 2026-04-16 22:51:15

85

Views

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

Published on 16 Apr 2026 - 22:51

score 116 · Answer 10 · 2026-04-16 00:18:00

116

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 16 Apr 2026 - 0:18

score 107 · Answer 11 · 2026-04-15 20:02:56

107

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 15 Apr 2026 - 20:02

score 97 · Answer 12 · 2026-04-15 06:40:45

97

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 15 Apr 2026 - 6:40

score 82 · Answer 13 · 2026-04-10 23:28:22

82

Views

System of functional equations

Published on 10 Apr 2026 - 23:28

score 79 · Answer 14 · 2026-04-14 04:44:27

79

Views

Can this fuctional equation be solved?

Published on 14 Apr 2026 - 4:44

score 143 · Answer 15 · 2026-05-04 18:35:51

143

Views

Functional Square Root of Digit Sum?

Published on 04 May 2026 - 18:35

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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