Show that $x^2 + y^2 = 3$ has no rational points
52960
Show that the curve $x^2+y^2-3=0$ has no rational points
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
36862
A question about proving that there is no greatest common divisor
106374
Show that $2x^6+12x^5+30x^4+60x^3+80x^2+30x+45=0$ has no real roots
151439
$\sqrt{1-x^2}$ is not a rational function
144802
Prove no solution to $x^2\equiv3\bmod5$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
145558
Prove that $2^n+3^n $ is never a perfect square
158933
Rational solutions of $y^2 = x^3 - x$
144863
Finding integer solutions to $y^2=x^3-2$
50760
Solutions to $y^2 = x^3 + k$?
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
94067
How prove this diophantine equation $x^2+y^2+z^3=n$ always have integer solution
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$