If $p$ is prime and $p|ab$, then $p|a$ or $p|b$.
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
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 $p|y^2−y+ 25$.
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
74370
$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
50412
Prime elements in $\mathbb{Z}/n\mathbb{Z}$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too