Prove that one of $2^n +1$ and $2^n-1$ must be composite for $n$ is a natural number greater than $2$
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
37315
not both $2^n-1,2^n+1$ can be prime.
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
3500
Compositeness of $n^4+4^n$
62177
Prove that: $2^n < n!$ Using Induction
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
143510
Prove that $n=\frac{5^{125}-1}{5^{25}-1}$ is a composite number
53751
Prove that $2^{10}+5^{12}$ is composite
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$