Why has $3^x+4^y=5^z$ has only one solution (2,2,2) in positive integers?
55248
Positive integral solutions of $3^x+4^y=5^z$
146753
Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
20834
Integer solutions to $c=a^2-b^2$
69874
Are there any integer solutions to $a^3=b^2$?
98408
Show that $x^2+y^2+z^2=999$ has no integer solutions
69328
(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
40063
$x^2+y^2=z^n$: Find solutions without Pythagoras!
137970
$2 + 2 = 5$ (Fake proof, or ?)
114489
Solving $x^p + y^p = p^z$ in positive integers $x,y,z$ and a prime $p$
41418
$2+2 = 5$? error in proof
25078
What is the solution set for the equation$ x ^ y = y ^ x$ in positive real numbers, x not equal to y?
32771
The equation $X^{n} + Y^{n} = Z^{n}$ , where $ n \geq 3$ is a natural number, has no solutions at all where $X,Y,Z$ are intergers.
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
114185
Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
150085
Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$
119109
Integer solutions to $ n^2 + 1 = 2 \times 5^m$
113268
Proving $x^4+y^4=z^2$ has no integer solutions