For any prime number $p$ and natural number $i < p$, prove that $p$ divides ${p \choose i}$.
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
101882
Does this polynomial evaluate to prime number whenever $x$ is a natural number?
77430
Prove that every prime larger than $3$ gives a remainder of $1$ or $5$ if divided by $6$
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
37947
Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.
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 $0<|x|,|y|<\sqrt{p}$
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
75733
Divisibility of prime numbers
53194
Prove : $p$(n│even number of ODD parts)=$p$(n│distinct parts ,number of ODD parts is even )
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
54547
Prove this number must be a prime number or 1.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
15348
prime divisor of $3n+2$ proof
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
108746
Prove that there exist two integers such that i - j is divisible by n.