Show the $n$th prime is $\le 2^{2^n}$
68688
n-th prime number is less than $4^n$
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
30374
If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
73515
Primes Number Theory
135614
Show that $2^n > n^2$ whenever n>4.
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
37947
Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.
20467
Show that $(y_n)\in l^q$
139383
Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.
50412
Prime elements in $\mathbb{Z}/n\mathbb{Z}$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
131488
Show that $p^3+4$ is prime
52427
Prove, $\sqrt{n} \le (n!)^\frac{1}{n} \le \frac{n+1}{2} $