Prove that $x^2+y^2=z^n$ has a solution in $N$ for all $n \in N$
40063
$x^2+y^2=z^n$: Find solutions without Pythagoras!
35504
The Diophantine equation $x^2 + 2 = y^3$
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
92106
Prove that $n$ is a sum of two squares?
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
66256
Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
85917
Solve $(x+1)^y-x^z=1$
148570
Find the all possible real solutions of $x^y=y^x$
27911
How can I prove that $xy\leq x^2+y^2$?
117352
Show $x^n+ax+b=0$ has most two solutions
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
18203
Diophantine equation $a^2+b^2=c^2+d^2$