$a^n +1$ prime, then $a$ is even and $n$ is a power of $2$
2802
If $2^n+1$ is prime, why must $n$ be a power of $2$?
43048
When is $2^n \pm 1$ a perfect power
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
113002
Any power of $(X_1, X_2,...,X_i)$ is primary in $k[X_1, X_2,...,X_n].$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
35553
If $n$ is composite, so is $2^n-1$
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
47162
Proving there are infinitely many primes of the form $a2^k+1.$
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$