Help proving ${n \choose k} \equiv 0 \pmod n$ for all $k$ such that $0<k<n$ iff $n$ is prime.
130615
divisibility of binomial coefficients by primes
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
13739
For all $n>2$ there exists a prime number between $n$ and $ n!$
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
58905
Proving infintely many primes of the form 6k-1
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
29640
If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
32463
$ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$