Primality of $2^n - 1$
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
43940
Showing that $n$ is pseudoprime to the base $a$
54442
Sum of $k {n \choose k}$ is $n2^{n-1}$
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
10742
Powers of prime factors of a positive integer $n$ in "Mathematica"?
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
120554
highest power of prime $p$ dividing $\binom{m+n}{n}$
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
57275
On the primality of integers of the form $p^2+k$
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
23606
Prime divisors of the integer $n^2+n-1$ (using the Legendre symbol)
55266
Prove that $(n+1)^{n-1}<n^n$