By considering z[sqrt[-2]] show that x^2+2=y^3 only has two integer solutions
53503
Solving the diophantine equation $y^{2}=x^{3}-2$
145287
Solve for integers $x, y, z$ such that $x + y = 1 - z$ and $x^3 + y^3 = 1 - z^2$.
21679
Solving $x^3-y^3=xy+61$ in integers
26461
Integer solutions of $x^3-x+9=5y^2$
66256
Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
63194
Find all integer solutions to $x^2-2y^2=1$
1001
Number of integer solutions of $x^2 + y^2 = k$
35504
The Diophantine equation $x^2 + 2 = y^3$
72023
Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
143194
How would you solve the diophantine $x^4+y^4=2z^2$
81854
Prove $x^4 + 131 = 3y^4$ has no integer solutions
113386
Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$
143281
How to solve $z^2-(1-3i)z-2i-2=0$
41689
Find all solutions: $x^2 + 2y^2 = z^2$
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
123159
Solutions of the diophantine equation $x+y+z=xyz$?