Find $F$ such that $F*F$ =P
56327
How to find the square root of a permutation
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
104278
Finding function $f(x)$ which satisfy given functional equation
18950
Show that $f$ has at most one fixed point
57639
Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
153869
Under what $p$, $-1$ is a square in $\mathbf F_p$?
81799
Examples of functions where $f(ab)=f(a)+f(b)$
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
121957
Is $p\mapsto \|f\|_p$ continuous?
19202
$\mathbb{F}_{p^d}\subseteq\mathbb{F}_{p^n}$ if and only if $d$ divides $n$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
84143
Given any function $g(x): \mathbb{R} \rightarrow \mathbb{R}$, find a function $f(x)$ such that $f(f(x)) = g(x)$.
120960
$f,g$ such that $\int fg = \int f \int g$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$