$p^2=2q^2$ $ p,q \in \mathbb {N} $ ??
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
131141
Solutions to $p+1=2n^2$ and $p^2+1=2m^2$ in Natural numbers.
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
115004
If $x\notin\mathbb Q$, then $\left|x-\frac{p}{q}\right|<\frac{1}{q^2}$ for infinitely many $\frac{p}{q}$?
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
43219
If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
82571
Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
137230
Find all pairs of primes $p,q$ such that $pq \mid 2^p +2^q$
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
64878
Is this polynomial irreducible in $\mathbb{Q}$?
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
7894
Does it follow that $(n!)^n$ divide $(n^2)!$
20034
Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
158148
Find all polynomials $P(x)$ such that $P(x^2)=P(x)^2$
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$