Prove that there is no uniqueness of factorisation in $\mathbb{Z}[\sqrt{10}]$.
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
10514
Proof that no polynomial with integer coefficients can only produce primes
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
144592
how to prove the existence and uniqueness of the prime factorization of any natural number.
146980
Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
93196
$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
63313
Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$
86922
Ring with 10 elements is isomorphic to $\mathbb{Z}/10 \mathbb{Z} $
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
45911
Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$