Prove that $y^2z^2 - y^2 -z^2$ is not a perfect square for any $y,z \in \mathbf{N}$
13120
Find all integer solutions to $x^2+y^2+z^2=2xyz$
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
86807
The units of $\mathbb Z[\sqrt{2}]$
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
59653
$x^2-y^2=2s$, s cannot be an odd integer
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
46102
Prove that $2^n +1$ in never a perfect cube
148101
Basis for $\mathbb{Z}^2$
57368
Prove that a positive polynomial function can be written as the squares of two polynomial functions
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
142513
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
67968
When is $2^n -7$ a perfect square?