Conjecture: Is the identity $2^5-5^2=2+5$ unique?
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
60615
Product of $5$ consecutive integers cannot be perfect square
147485
A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.
138569
Is the “sum of all natural numbers” unique?
10589
How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
120699
Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$?
91113
$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $
39739
Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$
114379
Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
82083
Solving $(z+1)^5 = z^5$
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
70522
$y^2 = \frac{x^5 - 1}{x-1}$ & $x,y \in \mathbb{Z}$
39698
On uniqueness of sums of prime powers
147666
How to prove that either $2^{500} + 15$ or $2^{500} + 16$ isn't a perfect square?
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined