Find all $n,k \in \Bbb N^+$ such that $(n-1)!=n^k-1$
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
91451
find all positive integer $m,n$
6539
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
81729
Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion
139659
Find all $n$ with $\!\bmod n\!:\, a\,$ invertible $\Rightarrow a^{-1} \equiv a,\,$ i.e. $a^2\equiv 1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
80216
Prove if $n \in \mathbb N$, then $\frac{1}{2!}+\cdots+\frac{n}{(n+1)!}=1-\frac{1}{(n+1)!}$
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
9217
Find $n$ such that $x^2 + x + 1$ is a factor of $(x+1)^n - x^n - 1$.
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$