Show that $y^2=x^3+23$ has no integer solutions (hint: use $y^2+4$)
66256
Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$
59653
$x^2-y^2=2s$, s cannot be an odd integer
113359
Proving that $x^2 + 4$ is not divisible by $3$
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
53503
Solving the diophantine equation $y^{2}=x^{3}-2$
144863
Finding integer solutions to $y^2=x^3-2$
122920
Why is $y + x = 3$ not the same as $y^2 + x^2 = 9$
142642
$A=\begin{pmatrix}0&0&1\\ 0&1&0\\ 1&0&0\end{pmatrix}$, $X^2=A$ has no solutions
143194
How would you solve the diophantine $x^4+y^4=2z^2$
7279
$|2^x-3^y|=1$ has only three natural pairs as solutions
145287
Solve for integers $x, y, z$ such that $x + y = 1 - z$ and $x^3 + y^3 = 1 - z^2$.
113268
Proving $x^4+y^4=z^2$ has no integer solutions
95490
What are the positive integer solutions to $x^2-x+1 = y^3$?
94067
How prove this diophantine equation $x^2+y^2+z^3=n$ always have integer solution
46028
Show that the solution for the Diophantine equation $x^2 - y^2 = N$ is unique if and only if $|N|$ or $\frac{|N|}{4}$, respectively, is $1$ or prime.
149254
Solving $y^3=x^3+8x^2-6x+8$