Smallest n>0 such that $2001^n-1\:%$ is divisible by $\:2^{2002}$
73025
Find min natural number $n$ so that $2^{2002}$ divides $2001^{n}-1$
44076
Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$
103150
Proof that $1729$ is the smallest taxicab number
128566
Proving $2$ generates $(\mathbb{Z}/19\mathbb{Z})^*$ by only looking at a few powers
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
31708
Divisibility criteria for $7,11,13,17,19$
86902
Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$...
33737
Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?
34960
Lower bound for $\phi(n)$: Is $n/5  1$?
35096
Is the $n$-th prime smaller than $n(\log n + \log\log n-1+\frac{\log\log n}{\log n})$?
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
96062
Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$
1409
Proving that the given set has at most $2^{n-1}$ elements
79187
Can we find $c_n$ to make $X_nc_n \rightarrow 0$ almost surely, even if $EX_n > \infty$?
153949
Is there a "smallest" divergent sum?
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
84491
Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.