Proof that $x^y=y^x$ is only true for the ordered pairs $(2,4)$ and $(4,2)$
5595
$x^y = y^x$ for integers $x$ and $y$
86567
Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
142513
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
17176
Proof that $x^n \mod b = (x \mod b)^n$
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
153123
Proving by induction $4^n  0$
71358
A very interesting question: intersection point of $x^y=y^x$
113268
Proving $x^4+y^4=z^2$ has no integer solutions
7279
$|2^x-3^y|=1$ has only three natural pairs as solutions
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
125707
A simple proof (hopefully) for $2^x \neq 0$
145397
How to prove that for every $i$, $a_i = i$
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$