Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
20705
On equations $m^2+1=5^n$
139659
Find all $n$ with $\!\bmod n\!:\, a\,$ invertible $\Rightarrow a^{-1} \equiv a,\,$ i.e. $a^2\equiv 1$
140140
An identity which applies to all of the natural numbers
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
108504
Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
142008
Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
151636
Fast way to calculate n! mod m where m is prime?
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
4530
For which natural numbers are $\phi(n)=2$?
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
31698
$f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers