Prove by contradiction that any prime number is either in the from of $ab+1$ or $ab+5$.
77430
Prove that every prime larger than $3$ gives a remainder of $1$ or $5$ if divided by $6$
144592
how to prove the existence and uniqueness of the prime factorization of any natural number.
56229
On the difference between consecutive primes
10425
Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
123296
Determine whether a number is prime
81267
A simple doubt in number theory problem.
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
128634
Doubt related to a theorem in congruences of Chapter 5 of Apostol Introduction to analytic number theory
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
50412
Prime elements in $\mathbb{Z}/n\mathbb{Z}$
85042
Write $1/1 + 1/2 + ...1/ (p-1)=a/b$ with $(a,b)=1$. Show that $p^2 \mid a$ if $p\geq 5$ is prime [Wolstenholme's theorem]
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.