Question

Find all multiplicative continuous functions on $(0,\infty)$

score 761 · Answer 1 · 2016-08-13 16:59:08

761

Views

Find all multiplicative continuous functions on $(0,\infty)$

Published on 13 Aug 2016 - 16:59

score 172 · Answer 2 · 2016-08-14 07:39:56

172

Views

To find all functions $h:\mathbb{R}\to\mathbb{R}$ such that $h(x+y) = h(x)+h(y)$ and $h(xy)=h(x)h(y)$

Published on 14 Aug 2016 - 7:39

score 185 · Answer 3 · 2016-08-16 10:47:35

185

Views

What completes the Dirichlet generating function $\zeta(s+c-1)$ where $c$ is a constant?

Published on 16 Aug 2016 - 10:47

score 976 · Answer 4 · 2026-03-25 22:03:29

976

Views

What is the symmetric functional equation of the Dirichlet eta function?

Published on 25 Mar 2026 - 22:03

score 67 · Answer 5 · 2016-08-18 08:50:47

67

Views

Solving $P(P(X)) = X^n+1$ over the polynomials.

Published on 18 Aug 2016 - 8:50

score 349 · Answer 6 · 2016-08-21 07:55:11

349

Views

Find all functions $f:[0;1]\rightarrow[0;1]$ which satisfying the following conditions: $f(0)=0, f(1)=1$ $f(x+y)-f(x)=f(x)-f(x-y)$

Published on 21 Aug 2016 - 7:55

score 302 · Answer 7 · 2026-03-25 13:34:19

302

Views

Determine all $P(X)\in K[X]$ such that $P\big(X^2+1\big)=\big(P(X)\big)^2+1$, for fields $K$ of any characteristic.

Published on 25 Mar 2026 - 13:34

score 122 · Answer 8 · 2016-08-25 16:26:37

122

Views

can we just check an obvious solution of a functional equation?

Published on 25 Aug 2016 - 16:26

score 150 · Answer 9 · 2016-08-28 08:25:29

150

Views

Does there exist a non-constant function $f:\mathbb N^2 \rightarrow \mathbb N$ such that $f(x,y)+f(y,x)=f(x^2,y^2)+1$

Published on 28 Aug 2016 - 8:25

score 4.4k · Answer 10 · 2026-03-29 19:09:16

4.4k

Views

Can there be an injective function whose derivative is equivalent to its inverse function?

Published on 29 Mar 2026 - 19:09

score 109 · Answer 11 · 2026-03-26 11:18:16

109

Views

Stone-Cech extension of a function satisfying $f(x+y)=f(x)+f(y)$?

Published on 26 Mar 2026 - 11:18

score 72 · Answer 12 · 2016-08-31 14:22:00

72

Views

Recursive function definition

Published on 31 Aug 2016 - 14:22

score 39 · Answer 13 · 2026-03-30 06:14:11

39

Views

Paley-Winer theorem

Published on 30 Mar 2026 - 6:14

score 3.9k · Answer 14 · 2016-09-03 15:28:14

3.9k

Views

Find all polynomials $p$ such that $p(x+1)=p(x)+2x+1.$

Published on 03 Sep 2016 - 15:28

score 132 · Answer 15 · 2026-03-25 23:42:31

132

Views

If $f(0,0) = f(\infty,0)=f(0,\infty) = 1$, but $f(\infty,\infty) = 0$, then what is $f(a,b)$?

Published on 25 Mar 2026 - 23:42

List Question

Find all multiplicative continuous functions on $(0,\infty)$

To find all functions $h:\mathbb{R}\to\mathbb{R}$ such that $h(x+y) = h(x)+h(y)$ and $h(xy)=h(x)h(y)$

What completes the Dirichlet generating function $\zeta(s+c-1)$ where $c$ is a constant?

What is the symmetric functional equation of the Dirichlet eta function?

Solving $P(P(X)) = X^n+1$ over the polynomials.

Find all functions $f:[0;1]\rightarrow[0;1]$ which satisfying the following conditions: $f(0)=0, f(1)=1$ $f(x+y)-f(x)=f(x)-f(x-y)$

Determine all $P(X)\in K[X]$ such that $P\big(X^2+1\big)=\big(P(X)\big)^2+1$, for fields $K$ of any characteristic.

can we just check an obvious solution of a functional equation?

Does there exist a non-constant function $f:\mathbb N^2 \rightarrow \mathbb N$ such that $f(x,y)+f(y,x)=f(x^2,y^2)+1$

Can there be an injective function whose derivative is equivalent to its inverse function?

Stone-Cech extension of a function satisfying $f(x+y)=f(x)+f(y)$?

Recursive function definition

Paley-Winer theorem

Find all polynomials $p$ such that $p(x+1)=p(x)+2x+1.$

If $f(0,0) = f(\infty,0)=f(0,\infty) = 1$, but $f(\infty,\infty) = 0$, then what is $f(a,b)$?

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