Show that the equation $x^2+y^2+z^2=2xyz$ has no integer solutions except $x=y=z=0$ using modular arithmetic
72023
Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
89677
Why there isn't any integer solutions in non-zero integers for $z^3 = 3(x^3 +y^3+2xyz)$?
61022
Diophantine Equations : Solving $a^2+ b^2=2c^2$
41689
Find all solutions: $x^2 + 2y^2 = z^2$
114489
Solving $x^p + y^p = p^z$ in positive integers $x,y,z$ and a prime $p$
143194
How would you solve the diophantine $x^4+y^4=2z^2$
108035
solving diophantine equations using congruences
73160
Solving the Diophantine Equation $x^2 - y! = 2001$ and $x^2 - y! = 2016$
50182
Prove the Mordell's equation $x^2+41=y^3$ has no integer solutions
53503
Solving the diophantine equation $y^{2}=x^{3}-2$
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution
77024
Find the number of solutions of $x^2=x\mod m$ for any integer $m$
74229
$2x^2+3y^2=z^2$ does not have a non-zero integral solution.
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
147442
Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
35504
The Diophantine equation $x^2 + 2 = y^3$
19071
solution set for congruence $x^2 \equiv 1 \mod m$