Integer solutions to $a^b = b^a$
5595
$x^y = y^x$ for integers $x$ and $y$
13120
Find all integer solutions to $x^2+y^2+z^2=2xyz$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
77024
Find the number of solutions of $x^2=x\mod m$ for any integer $m$
59091
A quartic diophantine equation
55100
The positive integer solutions for $2^a+3^b=5^c$
1001
Number of integer solutions of $x^2 + y^2 = k$
117352
Show $x^n+ax+b=0$ has most two solutions
19071
solution set for congruence $x^2 \equiv 1 \mod m$
82938
$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
144863
Finding integer solutions to $y^2=x^3-2$
69328
(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
95490
What are the positive integer solutions to $x^2-x+1 = y^3$?
94105
Find the all positive integer solutions $(a,b)$ to $\frac{a^3+b^3}{ab+4}=2020$.
97150
Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$.
85449
Show a,b,c congruences when $a^2+b^2=c^2$
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$