Find all the entire functions satisfying $f^2+g^2=1$
94597
$f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$
124971
Find all holomorphic functions with $\Re(f(x+iy))=2xy$
6680
Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
59196
Find all real solutions for $x$ in $ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2 . $
90261
Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
91085
how to find $|GL_2(F_p)|$
62251
"Maximum common divisor" for entire functions
12910
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
128477
Entire function constant, where $f(z)=f(z+1)$ and $|f(z)|< e^{|z|}$.
17700
Find all possible functions, $F(r)$, harmonic in $2$ and $3$ dimensions,
5625
Entire function with vanishing derivatives?
88333
Find all integral solutions of $y^2=x^3+7$
114245
What might I use to show that an entire function with positive real parts is constant?
144539
Power series $ f(g(z)) = z $
10253
Proving that all entire & injective functions take the form $f = ax + b$?
4296
If $f,g$ are entire functions and$\ fg\equiv 0$ then either $f \equiv 0$ or $g\equiv0. $
119869
Entire function and the series of its successive derivatives