Question

Finding all $ f : \mathbb Z \to \mathbb Z $ that satisfy $ f ( 0 ) = 1 $, $ f \big( f ( x ) \big) = x $ and $ f \big( f ( x + 1 ) + 1 \big) = x $

score 1.2k · Answer 1 · 2014-04-14 15:30:35

Finding all $ f : \mathbb Z \to \mathbb Z $ that satisfy $ f ( 0 ) = 1 $, $ f \big( f ( x ) \big) = x $ and $ f \big( f ( x + 1 ) + 1 \big) = x $

score 158 · Answer 2 · 2014-04-14 16:12:39

158

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Find all polynomials p with real coefficients

Published on 14 Apr 2014 - 16:12

score 562 · Answer 3 · 2014-04-15 22:49:51

562

Views

Help with functional equation $F(x,x)+F(x,c-x)-F(c-x,x)-F(c-x,c-x)=0$

Published on 15 Apr 2014 - 22:49

score 1.2k · Answer 4 · 2014-04-18 09:12:22

1.2k

Views

Suppose a function $f : \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(f(f(x)))=x$ for all $x$ belonging to $\mathbb{R}$.

Published on 18 Apr 2014 - 9:12

score 97 · Answer 5 · 2014-04-20 12:56:03

97

Views

Prove That $f(n+f(n))=n$

Published on 20 Apr 2014 - 12:56

score 3.2k · Answer 6 · 2014-04-22 02:45:51

3.2k

Views

Inverse Function Differential Equation

Published on 22 Apr 2014 - 2:45

score 51 · Answer 7 · 2014-04-23 07:37:17

51

Views

Functional equation on a ring

Published on 23 Apr 2014 - 7:37

score 413 · Answer 8 · 2014-04-24 05:38:41

413

Views

The "trick" in the Herglotz trick

Published on 24 Apr 2014 - 5:38

score 68 · Answer 9 · 2026-03-26 06:05:21

68

Views

Largest value in the functional $\int_0^\infty e^{-rt}( x^2+2x+\dot x^2)dt$?

Published on 26 Mar 2026 - 6:05

score 4.1k · Answer 10 · 2014-04-28 11:25:30

4.1k

Views

Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square

Published on 28 Apr 2014 - 11:25

score 2k · Answer 11 · 2014-04-28 12:17:48

2k

Views

A function such that $f(f(n)) = -n$?

Published on 28 Apr 2014 - 12:17

score 860 · Answer 12 · 2014-04-29 22:50:35

860

Views

Proof of continuity $f(x+y) = f(x) + f(y)$

Published on 29 Apr 2014 - 22:50

score 194 · Answer 13 · 2026-03-25 12:13:46

194

Views

submodular-like functions on $\mathbb{R}$

Published on 25 Mar 2026 - 12:13

score 54 · Answer 14 · 2014-05-01 20:03:15

54

Views

Is determining a non-constant solution to a functional inequality with polynomial arguements decidable?

Published on 01 May 2014 - 20:03

score 150 · Answer 15 · 2014-05-02 17:01:54

150

Views

Determine the smallest number P

Published on 02 May 2014 - 17:01

List Question

Finding all $ f : \mathbb Z \to \mathbb Z $ that satisfy $ f ( 0 ) = 1 $, $ f \big( f ( x ) \big) = x $ and $ f \big( f ( x + 1 ) + 1 \big) = x $

Find all polynomials p with real coefficients

Help with functional equation $F(x,x)+F(x,c-x)-F(c-x,x)-F(c-x,c-x)=0$

Suppose a function $f : \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(f(f(x)))=x$ for all $x$ belonging to $\mathbb{R}$.

Prove That $f(n+f(n))=n$

Inverse Function Differential Equation

Functional equation on a ring

The "trick" in the Herglotz trick

Largest value in the functional $\int_0^\infty e^{-rt}( x^2+2x+\dot x^2)dt$?

Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square

A function such that $f(f(n)) = -n$?

Proof of continuity $f(x+y) = f(x) + f(y)$

submodular-like functions on $\mathbb{R}$

Is determining a non-constant solution to a functional inequality with polynomial arguements decidable?

Determine the smallest number P

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