Find all $d > 0$ that for any function $f$ such as $f(0) = f(1)$ for some $x_0 \in [0, 1 - d]$ $f(x_0) = f(x_0 + d)$
12632
Universal Chord Theorem
86128
Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
97371
Proving a function is constant, under certain conditions?
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
26754
Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
129052
Find all functions satisfying $\frac{1}{f(a)}+ \frac{1}{f(b)} = \frac{1}{f(c)} $ whenever $\frac{1}{a}+ \frac{1}{b} = \frac{1}{c} $
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
42699
Solve for $f(x)$ if $f(f(x))=6x-f(x)$
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$