Prove that $x^2=-1$ has no solution in $\mathbb Z$.
101169
Prove that $x^2 = - 1$ has no solution in $\mathbb{Z}$
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
110826
prove that : $ i = \sqrt {-1}\ $
146980
Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution
134834
$n^2 + (n+1)^2 = m^3$ has no solution in the positive integers
144802
Prove no solution to $x^2\equiv3\bmod5$
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
98408
Show that $x^2+y^2+z^2=999$ has no integer solutions
126494
Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
95057
Possible fake proof of $1= -1$
135087
Find integer solutions of $xy=-1$ (using only elementary ring theory).
49453
Why do I have to solve for $x$ in this proof, if I choose not to find a counterexample?
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.