Show that $x^2+y^2 = 3$ has no rational solutions
87994
Find rational points on $x^2 + y^2 = 3$ and on $x^2 + y^2 = 17$
110195
$p=4n+3$ never has a Decomposition into $2$ Squares, right?
43537
How can $x^2y''-3xy'+3y=0$ be solved?
155743
Why does the equation $x^2\equiv2 \pmod 5$ have no solutions?
21679
Solving $x^3-y^3=xy+61$ in integers
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
2648
Show that the equation $\cos(\sin x)=\sin(\cos x)$ has no real solutions.
22112
Find all integer solutions to $x^2+4=y^3$.
69874
Are there any integer solutions to $a^3=b^2$?
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
148243
Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.
50760
Solutions to $y^2 = x^3 + k$?
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
148310
Showing rational numbers are algebraic
70692
Solve $x^2+2=y^3$ using infinite descent?