Let $r\in\mathbb{Q}$. If $r^2\in\mathbb{Z}$ then $r\in\mathbb{Z}$.
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
78917
Show that for any prime numbers $p,q,r$, one has $p^2+q^2 \ne r^2$.
148101
Basis for $\mathbb{Z}^2$
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
39217
If $d \mid n$ then $x^{q^d} - x \mid x^{q^n} - x$.
88523
Show that $A=\{ \frac{m}{2^n}:m\in \mathbb {Z},n\in \mathbb {N} \} $ is dense in $\mathbb {R}$
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
91113
$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
27670
Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$