If $a\mid b$ then $\phi(a)\mid \phi(b)$ for $a,b\in\mathbb{N}$
100515
Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
120629
Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them
104549
When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$
61858
Is there $\phi(n)=n/6$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
12100
$n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
39953
$a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
13026
Prove that if AB=I_m, then rk(A)=rk(B).