Question

For $n\in\mathbb{Z^+}$ unique $f(n)\in\mathbb{Z^+}$ is mapped with $f(1)=1$, $f(f(n))=n$ and $f(2n)=2f(n)+1$. Find $f(2020)$.

score 98 · Answer 1 · 2026-04-16 13:21:36

98

Views

For $n\in\mathbb{Z^+}$ unique $f(n)\in\mathbb{Z^+}$ is mapped with $f(1)=1$, $f(f(n))=n$ and $f(2n)=2f(n)+1$. Find $f(2020)$.

Published on 16 Apr 2026 - 13:21

score 95 · Answer 2 · 2026-04-09 02:25:29

95

Views

Heterogeneous diffusion process

Published on 09 Apr 2026 - 2:25

score 152 · Answer 3 · 2026-04-14 23:45:44

152

Views

Pseudo-periodicity of analytic self-maps of the upper half-plane

Published on 14 Apr 2026 - 23:45

score 63 · Answer 4 · 2026-04-12 17:14:46

63

Views

How do I prove that the equation $f(x) = x + \frac{1}{4}\cos(x)\int_{0}^{\frac{\pi}{2}}f(y)dy$ has a unique solution?

Published on 12 Apr 2026 - 17:14

score 92 · Answer 5 · 2026-04-16 06:21:44

92

Views

Is there a simpler function $f$ equivalent to $f(x)=af(x-1)^2+bf(x-1)+c$?

Published on 16 Apr 2026 - 6:21

score 239 · Answer 6 · 2026-04-16 16:22:39

239

Views

Find all polynomials $P$ such that $P(P(x))=P(x^n)+P(x)-1$

Published on 16 Apr 2026 - 16:22

score 86 · Answer 7 · 2026-04-12 15:20:29

86

Views

Functional equation $(x-y)(f(x)+f(y))=(x+y)f(x-y)$

Published on 12 Apr 2026 - 15:20

score 146 · Answer 8 · 2026-04-16 19:06:49

146

Views

Find all polynomials $P, Q$ such that $(x^2+ax+b)P(x^2+cx+d)=(x^2+cx+d)Q(x^2+ax+b)$

Published on 16 Apr 2026 - 19:06

score 70 · Answer 9 · 2026-04-15 05:55:24

70

Views

A simple difference equation or functional equation that has a solution $(ax+b)^c$

Published on 15 Apr 2026 - 5:55

score 68 · Answer 10 · 2026-04-12 23:24:48

68

Views

Partial Differential Equation with boundary dirichlet conditions without solutions

Published on 12 Apr 2026 - 23:24

score 131 · Answer 11 · 2026-04-16 06:56:32

131

Views

$f(x) = f^{-1}(x) \Rightarrow f(x) = x$?

Published on 16 Apr 2026 - 6:56

score 75 · Answer 12 · 2026-04-16 13:06:46

75

Views

Prove/disprove that there are functions $f$ and $g$ that keep the condition, so that if $f$ is surjective and $g$ is injective.

Published on 16 Apr 2026 - 13:06

score 150 · Answer 13 · 2026-04-16 17:48:56

150

Views

If $\;f(x)+\frac{1}{x}=f^{-1}(\frac{1}{f(x)})\;$ and $f^{-1}(\frac{1}{f(x)})>0$. Then $f(x)$ is?

Published on 16 Apr 2026 - 17:48

score 59 · Answer 14 · 2026-04-12 20:20:39

59

Views

Functions satisfying the below functional equations

Published on 12 Apr 2026 - 20:20

score 143 · Answer 15 · 2026-04-10 16:23:13

143

Views

Is the identity function the only solution for $f(a^x)=a^{f(x)}$?

Published on 10 Apr 2026 - 16:23

List Question

For $n\in\mathbb{Z^+}$ unique $f(n)\in\mathbb{Z^+}$ is mapped with $f(1)=1$, $f(f(n))=n$ and $f(2n)=2f(n)+1$. Find $f(2020)$.

Heterogeneous diffusion process

Pseudo-periodicity of analytic self-maps of the upper half-plane

How do I prove that the equation $f(x) = x + \frac{1}{4}\cos(x)\int_{0}^{\frac{\pi}{2}}f(y)dy$ has a unique solution?

Is there a simpler function $f$ equivalent to $f(x)=af(x-1)^2+bf(x-1)+c$?

Find all polynomials $P$ such that $P(P(x))=P(x^n)+P(x)-1$

Functional equation $(x-y)(f(x)+f(y))=(x+y)f(x-y)$

Find all polynomials $P, Q$ such that $(x^2+ax+b)P(x^2+cx+d)=(x^2+cx+d)Q(x^2+ax+b)$

A simple difference equation or functional equation that has a solution $(ax+b)^c$

Partial Differential Equation with boundary dirichlet conditions without solutions

$f(x) = f^{-1}(x) \Rightarrow f(x) = x$?

Prove/disprove that there are functions $f$ and $g$ that keep the condition, so that if $f$ is surjective and $g$ is injective.

If $\;f(x)+\frac{1}{x}=f^{-1}(\frac{1}{f(x)})\;$ and $f^{-1}(\frac{1}{f(x)})>0$. Then $f(x)$ is?

Functions satisfying the below functional equations

Is the identity function the only solution for $f(a^x)=a^{f(x)}$?

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