Prove that $x² + y² = z^n$ has a solution in $\mathbb{N}$, for all $n$ belonging to the set of natural numbers
40063
$x^2+y^2=z^n$: Find solutions without Pythagoras!
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
89175
Proof of $(a+b)^{n+1}$
99739
The diophantine equation $x^2+y^2=3z^2$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
143113
Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
20964
Proof that $n^2 < 2^n$
10753
Natural number solutions to $\frac{xy}{x+y}=n$ (equivalent to $\frac 1x+\frac 1y=\frac 1n$)
152311
Proving expression$\geq 2$, where variables are $x,y,z$
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
133480
new addition and new multiplication x ⊕ y = x + y − 1, x ⊗ y = x + y − xy on set Z, prove the set Z equipped with these 2 new operation
38379
Showing that $e^z=z$ has infinitely many solutions
51417
Solve: $\overline{z}=z^n$
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.