Let $n\in \mathbb{Z}^+ $ s.t $n$ has no square factors other than 1. Prove that for any $x \in \mathbb{Z}$, $n|x^2 \implies n|x$
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
49621
Proof of "well-founded iff there is no sequence $x_n$ s.t. $(x_{n+1}, x_n) \in R$"
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
136077
Prove that $x-1$ is a factor of $x^n-1$
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
20964
Proof that $n^2 < 2^n$
96185
Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
27449
Product of Divisors of some $n$ proof
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
59134
Proving idempotent elements in $\mathbb{Z}_n$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $