Prove that $2^{n}+1$ is not a cube of an integer for all $n\in\mathbb{N}$
46102
Prove that $2^n +1$ in never a perfect cube
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
62177
Prove that: $2^n < n!$ Using Induction
981
If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
93948
Is my proof correct? $p_1p_2p_3\cdots p_n+1)$ cannot be the square of an integer
143113
Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$
66210
Prove that $z^n + 1/{z^n}$ is a rational number
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$