Reference request: there are only two integer solutions to $2^{2a} + 3^{2b} = 5^c$.
55248
Positive integral solutions of $3^x+4^y=5^z$
137652
How many solutions does the equation $n_1 + n_2 + n_3 + n_4 + n_5 = 20$ have in the positive integers if $n_1 < n_2 < n_3 < n_4 < n_5$?
26287
Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$
119109
Integer solutions to $ n^2 + 1 = 2 \times 5^m$
9542
Integer solutions for $x^2-y^3 = 23$.
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
144863
Finding integer solutions to $y^2=x^3-2$
53503
Solving the diophantine equation $y^{2}=x^{3}-2$
10589
How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
143501
Find all $n\in\mathbb N^+$ such that the sum of the digits of $5^n$ is equal to $2^n$.
134834
$n^2 + (n+1)^2 = m^3$ has no solution in the positive integers
156873
Solve the equation $\binom{2n+1}{n+2} = \binom{2n+1}{5} $
33469
Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
112575
Finding integer solutions of $m^2-n^5 = m - n$
32985
Prove that there does not exist integer solutions for the diophantine equation $x^5 - y^2 = 4$.
23270
The sum of powers of two and two's complement – is there a deeper meaning behind this?