For all $n$, there are integers $x$, $y$, $z$ such that $x^2 + y^2 = z^n$
40063
$x^2+y^2=z^n$: Find solutions without Pythagoras!
47809
If $x,y\in\mathbb Z$, solve $x^2+xy+y^2=x^2y^2$.
117392
Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
35504
The Diophantine equation $x^2 + 2 = y^3$
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
77564
How to prove for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$?
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
20486
Numbers representable as $x^2 + 2y^2$
72023
Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
92057
Prove that for every odd integer n, there is a group...
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
41689
Find all solutions: $x^2 + 2y^2 = z^2$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
92290
For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$