If $n$ is an $\underline{\text{integer}}$ > 7, prove that $\big(^n_7\big) - { \begin{bmatrix}{\frac {n}{7}} \end{bmatrix} }$ is divisible by $7$.
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
80365
Prove that $n$ is divisible by $6$
91914
Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.
133819
How to prove that $364 \mid n^{91} - n^7$?
124890
Divisibility within a block of natural numbers
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
113359
Proving that $x^2 + 4$ is not divisible by $3$
127720
Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
49501
Prove that : $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ divisible by $12$
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
125040
Show by induction : $n^7-n$ is a multiple of 7
149758
How to prove $\log n < n$?
3611
How to prove $n^5 - n$ is divisible by $30$ without reduction
31708
Divisibility criteria for $7,11,13,17,19$
117969
Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
126816
Question of remainder on dividing by 7
96062
Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$