For all integers $k$, $l$, $m$, $n$, if $k = nl + m$, then $n$ divides $k$ iff $n$ divides $m$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
127855
Show that the product of any $m$ consecutive positive integers is divisible by $m!$
49427
$l^2+m^2=n^2$ $\implies$ $lm$ is always a multiple of 3 when $l,m,n,$ are positive integers.
48452
Proof that $\gcd$ divides $\operatorname{lcm}$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
74523
Proof by Cases involving divisibility
108504
Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.
113248
Proving $r!$ divides the product of r succesive positive integers
148906
Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
91451
find all positive integer $m,n$
124456
Given $x \in \mathbb{R}$ and $N \in \mathbb{N}, N>1,$ find integers $h,k$ with $0 < k \leq N $ that satisfy $\lvert{kx - h\rvert} < 1/N.$
33810
Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
5577
If $m$ divides $n$, find a free resolution of $\mathbb{Z}/m$ as a $\mathbb{Z}/n$-module.