For any natural number $n$, exists $z,x,y\in\mathbb{N}$ such that: $z^n=x^2+y^2$
40063
$x^2+y^2=z^n$: Find solutions without Pythagoras!
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
22073
Prove by induction that $n^2<n!$
87345
How many ways so that $x+y+z\leq n$?
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
20964
Proof that $n^2 < 2^n$
158524
Complex numbers $z$ such that $|z|= 1$
35504
The Diophantine equation $x^2 + 2 = y^3$
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
82571
Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
66210
Prove that $z^n + 1/{z^n}$ is a rational number
94700
Integer solutions for $x^3+2=y^2$?
20486
Numbers representable as $x^2 + 2y^2$
35184
If $z_n \to z$ then $(1+z_n/n)^n \to e^z$
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
155757
Number theory: $x^y + 1 = y^x$