Proving $k$ is divisible by $3$ iff the sum of the digits of $k$ is divisible by 3
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
100892
Proving divisibility of $a^3 - a$ by $6$
70951
Prove divisibility law $\,b\mid a,c\,\Rightarrow\, b\mid ka + lc$ for all $k,l\in\Bbb Z$
118918
Understanding a proof that $2x + 3y$ is divisible by $17$ iff $9x + 5y$ is divisible by $17$
85817
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
96737
Geometric proof that a Pythagorean triple has a number divisible by $3$?
85941
Proof by induction that $n^3 - n$ is divisible by $6$
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
108746
Prove that there exist two integers such that i - j is divisible by n.
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$