Prove that $b-1 \mid a \iff b-1\mid s$
30496
Casting nines and elevens in other bases (radix) and doing check sums for binary
151852
How to prove $A \subset B \iff A \cup B = B$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
56512
Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$
114667
$d\mid a,b \iff d\mid\gcd(a,b) \ $ [GCD Universal Property]
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
119118
Prove $n\mid \phi(2^n-1)$
39175
Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?