Prove there is no nonzero integer solution to $x^2 - 2y^2 = 0$
43985
Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
52960
Show that the curve $x^2+y^2-3=0$ has no rational points
12150
For what value of m that the equation $y^2 = x^3 + m$ has no integral solutions?
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
6582
Prove the existence of the square root of $2$.
44744
Integer solutions of $xy+9(x+y)=2006$
24837
$x^2+1=0$ uncountable many solutions
5679
Why is $2\pi i \neq 0?$
18053
Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
125707
A simple proof (hopefully) for $2^x \neq 0$
134834
$n^2 + (n+1)^2 = m^3$ has no solution in the positive integers
117392
Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
158933
Rational solutions of $y^2 = x^3 - x$
88760
Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$