Why does the equation $x^4 -17 = 2y^2$ have no rational solution?
140378
Show that the curve $2Y^2 = X^4 - 17$ has no points in $\mathbb{Q}$
133680
On the equation $3x^3 + 4y^3 + 5z^3 = 0$
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
117392
Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
22112
Find all integer solutions to $x^2+4=y^3$.
44400
$e^{2\pi i x} = (e^{2\pi i})^x$: What happens if x is rational?
40087
Using Modularity Theorem and Ribet's Theorem to disprove existence of rational solutions
106242
Why no common factors in proving root 2 is irrational?
32985
Prove that there does not exist integer solutions for the diophantine equation $x^5 - y^2 = 4$.
95913
Solve for $x$: $2^x=4x$
101169
Prove that $x^2 = - 1$ has no solution in $\mathbb{Z}$
96647
Number theory: Problem involving rational numbers
77763
Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
142642
$A=\begin{pmatrix}0&0&1\\ 0&1&0\\ 1&0&0\end{pmatrix}$, $X^2=A$ has no solutions
81854
Prove $x^4 + 131 = 3y^4$ has no integer solutions
41689
Find all solutions: $x^2 + 2y^2 = z^2$
87029
Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$