$(b_n) \rightarrow b$ then $(1/b_n) \rightarrow 1/b$ proof.
61670
Proving that $(b_n) \to b$ implies $\left(\frac{1}{b_n}\right) \to \frac{1}{b}$
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
80144
Prove that $x-1$ divides $x^n-1$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
91829
Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
46286
Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers.
10236
Show that $a^n \mid b^n$ implies $a \mid b$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
25648
Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$