List questions from functional-equations

Published on 16 Apr 2020 - 14:34

134

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Find all polynomials $P(x)$ such that $2 P\left(2 x^{2}-1\right)=P(x)^{2}-2$

Published on 17 Apr 2020 - 14:18

50

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Is this function $f(x f(x)+y)=x^{2}+f(y)$ onto ??

Published on 18 Apr 2020 - 8:28

20

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Theorem about iterative roots from "Contributions to general algebra 6"

Published on 18 Apr 2020 - 13:01

50

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proving function is constant using periodicity

Published on 19 Apr 2020 - 10:06

40

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A functional equation problem calculus

Published on 19 Apr 2020 - 20:09

202

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Find all functions $f:$ $\mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ $ x^{2}(f(x)+f(y))=(x+y) f(f(x) y) $

Published on 20 Apr 2020 - 4:42

149

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Boundedness ,Additive and Cauchy

Published on 20 Apr 2020 - 6:38

156

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Find all $f: \mathbb{N} \rightarrow \mathbb{N}$ which satisfy $ f(m-n+f(n))=f(m)+f(n) $

Published on 20 Apr 2020 - 10:37

100

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

Published on 20 Apr 2020 - 15:57

181

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How to simplify this polylog expression $\operatorname{Li}_4\left(\frac{z-1}{z}\right)$?

Published on 26 Mar 2026 - 13:02

97

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Functional equation $f(x+1)+f(x-1)=\sqrt{2}\cdot f(x)$

Published on 20 Apr 2020 - 20:29

519

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How can I solve $f(t^2+u)=tf(t)+f(u)$

Published on 21 Apr 2020 - 8:00

140

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Easy but strange Olympiad functional equations

Published on 21 Apr 2020 - 8:49

219

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Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ which satisfy $ f\left(m^{2}+m n\right)=f(m)^{2}+f(m) f(n) $

Published on 21 Apr 2020 - 10:29

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IMO 2002 Problem 5 Solution doubt

Find all polynomials $P(x)$ such that $2 P\left(2 x^{2}-1\right)=P(x)^{2}-2$

Is this function $f(x f(x)+y)=x^{2}+f(y)$ onto ??

Theorem about iterative roots from "Contributions to general algebra 6"

proving function is constant using periodicity

A functional equation problem calculus

Find all functions $f:$ $\mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ $ x^{2}(f(x)+f(y))=(x+y) f(f(x) y) $

Boundedness ,Additive and Cauchy

Find all $f: \mathbb{N} \rightarrow \mathbb{N}$ which satisfy $ f(m-n+f(n))=f(m)+f(n) $

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

How to simplify this polylog expression $\operatorname{Li}_4\left(\frac{z-1}{z}\right)$?

Functional equation $f(x+1)+f(x-1)=\sqrt{2}\cdot f(x)$

How can I solve $f(t^2+u)=tf(t)+f(u)$

Easy but strange Olympiad functional equations

Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ which satisfy $ f\left(m^{2}+m n\right)=f(m)^{2}+f(m) f(n) $

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