Proving that $9$ is a divisor of $x \in \Bbb N$ if the sum of digits of $x$ is divisible by $9$.
3128
Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens)
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
85959
How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
105487
Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$
153302
$9$ divides $n-r(n)$ where $r(n)$ is $n$ with its digits reversed
134739
product of divisors of n as a power of n.
52032
Prove that ${n^5 - n}$ is divisible by 5
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
115145
Show that $n-m$ is a multiple of 9 when $n$ and $m$ have same digits
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
10744
Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3
140087
The number of divisors
150430
Let $S={1, 2, 3, 4, ....., 2070}$ find the number of subsets of $S$ whose sum of elements in $S$ is divisible by 9