If $x^m=y^n=e$ and $(m,n)=1$, then $o(xy)=mn$
11509
Relationship between $\operatorname{ord}(ab), \operatorname{ord}(a)$, and $\operatorname{ord}(b)$
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
133614
Why is $x^{\log_x n}=n$?
19599
$ d(x_n,y_n) \to d(x,y)$ if $x_n\to x$ and $y_n \to y$
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
38849
Solve $x^y \, = \, y^x$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
37346
If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$.
35066
Nature and number of solutions to $xy=x+y$
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
107397
Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
35184
If $z_n \to z$ then $(1+z_n/n)^n \to e^z$
104602
asymptotic of $x^{x^x} = n$
48332
Why does the minimum value of $x^x$ equal $1/e$?
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .