The number of divisors of any positive number $n$ is $\le 2\sqrt{n}$
52157
Prove that $d(n)\leq 2\sqrt{n}$
110444
Finding out the number of divisors
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
75516
Relatively Prime Numbers and Number of Divisors of n
18402
Sum of the reciprocals of divisors of a perfect number is $2$?
40131
If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
104447
Prove that $\sqrt{n} \le \sum_{k=1}^n \frac{1}{\sqrt{k}} \le 2 \sqrt{n} - 1$ is true for $n \in \mathbb{N}^{\ge 1}$
9302
Questions about Divisibility of $2^n$ by $3$
48268
How many $\alpha \in S_n$ are such that $\alpha^2 = 1$?
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
133528
$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$
44391
How can I prove $n - 2\sqrt{n} = \Theta(n)$
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
130842
Prime factors + number of Divisors
78985
Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$
54900
How to prove $|\sum_{i=1}^n a_i|\le \sqrt{n} \sqrt{\sum_{i=1}^n a_i^2}$