Question

Finding functions $h$ satisfying $h(h(n))+h(n+1) = n+2$ for all natural $n$. Why does the Golden Ratio appear?

score 115 · Answer 1 · 2026-03-26 11:17:52

115

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Finding functions $h$ satisfying $h(h(n))+h(n+1) = n+2$ for all natural $n$. Why does the Golden Ratio appear?

Published on 26 Mar 2026 - 11:17

score 78 · Answer 2 · 2024-03-22 06:15:44

78

Views

Functional equation over positive integers: $f(x + y) = f(x) + f(y) + 3(x + y)\sqrt[3]{f(x)f(y)}$

Published on 22 Mar 2024 - 6:15

score 66 · Answer 3 · 2024-03-25 17:50:30

66

Views

Proof that a certain function that satisfy a specific equation is constant

Published on 25 Mar 2024 - 17:50

score 519 · Answer 4 · 2024-03-26 05:19:15

519

Views

Why is this function almost Lipschitz?

Published on 26 Mar 2024 - 5:19

score 74 · Answer 5 · 2024-03-26 08:38:37

74

Views

Functional equation $x^n f(1/x) = f(x)$

Published on 26 Mar 2024 - 8:38

score 39 · Answer 6 · 2024-03-26 21:03:46

39

Views

Restriction of a linear map on a compact convex subset of $\mathbb R^n$ with non-empty interior

Published on 26 Mar 2024 - 21:03

score 17 · Answer 7 · 2026-03-13 04:38:44

17

Views

Recurrence relation with kernel convolution

Published on 13 Mar 2026 - 4:38

score 282 · Answer 8 · 2024-03-30 11:36:20

282

Views

Find all functions $ f(x^2+y^2) + f(xf(y) + f(x)f(y)) = (f(x+y))^2. $

Published on 30 Mar 2024 - 11:36

score 64 · Answer 9 · 2015-01-04 05:51:44

64

Views

All $f$ such that $(\exists k)(f^\prime(x) = f(x+k))$

Published on 04 Jan 2015 - 5:51

score 179 · Answer 10 · 2026-03-27 14:02:30

179

Views

Existance of solution to integral Fredholm equation

Published on 27 Mar 2026 - 14:02

score 203 · Answer 11 · 2015-01-06 14:41:59

203

Views

Is there a function $f(x)$ such that $f(f(x))=e^x$?

Published on 06 Jan 2015 - 14:41

score 6k · Answer 12 · 2015-01-06 17:06:46

6k

Views

A function that satisfies $f\left({\frac{x+y}3}\right)=\frac{f(x)+f(y)}2$ must be a constant

Published on 06 Jan 2015 - 17:06

score 3.2k · Answer 13 · 2015-01-06 19:17:40

3.2k

Views

Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$

Published on 06 Jan 2015 - 19:17

score 122 · Answer 14 · 2015-01-06 20:24:23

122

Views

When can we take that $f(1)=1$?

Published on 06 Jan 2015 - 20:24

score 515 · Answer 15 · 2026-03-28 15:12:46

515

Views

Is distributivity sufficient to define composition?

Published on 28 Mar 2026 - 15:12

List Question

Finding functions $h$ satisfying $h(h(n))+h(n+1) = n+2$ for all natural $n$. Why does the Golden Ratio appear?

Functional equation over positive integers: $f(x + y) = f(x) + f(y) + 3(x + y)\sqrt[3]{f(x)f(y)}$

Proof that a certain function that satisfy a specific equation is constant

Why is this function almost Lipschitz?

Functional equation $x^n f(1/x) = f(x)$

Restriction of a linear map on a compact convex subset of $\mathbb R^n$ with non-empty interior

Recurrence relation with kernel convolution

Find all functions $ f(x^2+y^2) + f(xf(y) + f(x)f(y)) = (f(x+y))^2. $

All $f$ such that $(\exists k)(f^\prime(x) = f(x+k))$

Existance of solution to integral Fredholm equation

Is there a function $f(x)$ such that $f(f(x))=e^x$?

A function that satisfies $f\left({\frac{x+y}3}\right)=\frac{f(x)+f(y)}2$ must be a constant

Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$

When can we take that $f(1)=1$?

Is distributivity sufficient to define composition?

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