Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
70463
Let $p$ be prime and $a$ be a natural not divisible by $p$. Then, $\exists$ integers $x,y$ such that $ax\equiv y \pmod{p}$ with $0<|x|,|y|<\sqrt{p}$
147101
Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
66019
Revisited: Binomial Theorem: An Inductive Proof
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
5206
Highest power of a prime $p$ dividing $N!$
79940
$\binom{p}{i}$ divisible by $p$, with $p$ prime
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
67650
Short and intuitive proof that $\left(\frac{n}{k}\right)^k \leq \binom{n}{k}$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$