If $3$ divides the decimal digit sum of $n$ then $3$ divides $n$ (casting out threes)
3128
Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens)
48053
Show that 13 divides $2^{70}+3^{70}$
91105
For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
36182
Why doesn't the last digit method work for divisibility by 4?
25338
Sum of $n$ integers from set of size $2n-1$ divides $n$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
62100
Show that $n^3-n$ is divisible by $6$ using induction
106847
Proof that $n^3+2n$ is divisible by $3$
122386
How do I prove that $3$ divides $14^{2n}-1$ by induction?
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
65328
Counts and skips the numbers that have digits divisible by 3 (change in base method)
49687
Show that the number 9 divides the number $ m$ if and only if the sum of the digits of the number $ m $ is divisible by 9.
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$