proof that (2,4) is the only natural solution to $x^y=y^x$.
5595
$x^y = y^x$ for integers $x$ and $y$
20626
Prove that $x^y < y^x$
74920
Prove that the equation $x^2-y^2 = 2002$ has no integer solution
87029
Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$
98408
Show that $x^2+y^2+z^2=999$ has no integer solutions
94700
Integer solutions for $x^3+2=y^2$?
113359
Proving that $x^2 + 4$ is not divisible by $3$
55206
Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square
125707
A simple proof (hopefully) for $2^x \neq 0$
153123
Proving by induction $4^n  0$
74713
Show that for any natural numbers, if $S(x)=S(y)$ then $x=y$.
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
25078
What is the solution set for the equation$ x ^ y = y ^ x$ in positive real numbers, x not equal to y?
65371
Does $2^X \cong 2^Y$ imply $X \cong Y$ without assuming the axiom of choice?
141184
Proof that a degree 4 polynomial has at least two roots
139288
Formal proof that $e^x$ is not algebraic
46028
Show that the solution for the Diophantine equation $x^2 - y^2 = N$ is unique if and only if $|N|$ or $\frac{|N|}{4}$, respectively, is $1$ or prime.