$\textbf Z[\sqrt{pq}]$ is not a UFD if $\left( \frac{q}p \right) = -1$ and $p \equiv 1 \pmod 4$.
58717
Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain
153869
Under what $p$, $-1$ is a square in $\mathbf F_p$?
62941
1/z on an annulus has no anti-derivative
42932
Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.
85398
$\mathsf{ZF}$ is not finitely axiomatizable
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
140106
How to prove a finite field is not ordered?
127396
When is $f=\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^5-3x+\ln5$ decreasing $\forall\; x$?
77735
When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
86025
Nonabelian semidirect products of order $pq$?
28987
One-dimensional [Noetherian] UFD is a PID
80826
To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
11935
Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean?
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus