For which positive integers $n$ is $2^n+1$ divisible by $n^2$
19254
How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers?
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
85817
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
68145
If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$
52032
Prove that ${n^5 - n}$ is divisible by 5
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
9302
Questions about Divisibility of $2^n$ by $3$
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$
17194
$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$
144132
The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.
77564
How to prove for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$?
108746
Prove that there exist two integers such that i - j is divisible by n.
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
148796
Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$