Help with understanding of proof of no rational points on $x^2+y^2=3$?
52960
Show that the curve $x^2+y^2-3=0$ has no rational points
115834
Cubic polynomial with three (distinct) irrational roots
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
130310
Elliptic curve $y^2= x^3 + x$ over the finite field $\mathbb{F}_p$ with $p \geq 3$.
133164
Rational solutions for $x^2+y^2=3$
144802
Prove no solution to $x^2\equiv3\bmod5$
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
94700
Integer solutions for $x^3+2=y^2$?
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
98440
Show that any non-negative rational integer may be written as the sum of two squares if it is of the form....
109953
How to prove that $\sqrt 3$ is an irrational number?
122226
Incorrect logic in popular proof of the irrationality of $\sqrt2$?
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
151439
$\sqrt{1-x^2}$ is not a rational function