Can $n - 1$ divide $n$, where $n$ is a positive, composite integer?
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
117761
When is $\binom{n}{k}$ divisible by $n$?
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
155886
let q be an odd prime and p a prime dividing $1+n+\dots+n^{q-1}$
63893
Prime dividing the binomial coefficients
72843
Parity of number of factors up to a bound?
116361
Relationship between prime factorizations of $n$ and $n+1$?
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
32754
Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
112182
Sequence of positive integers such that their reciprocals are in arithmetic progression
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
147079
$\gcd\left(\binom{n}{k},n\right)>1$ for nontrivial values?
25338
Sum of $n$ integers from set of size $2n-1$ divides $n$
134963
Proving a non-prime (composite) number $> 1$ has a divisor $d \leq\sqrt q$
65757
Prove that $n! + k$ is a composite number
35096
Is the $n$-th prime smaller than $n(\log n + \log\log n-1+\frac{\log\log n}{\log n})$?
16660
Prove that any positive number has an $n$th root