Prove: 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 $p \mid b$.
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
34478
If $P(A \mid E) > P(B \mid E)$ and $P(A \mid \neg E) > P(B \mid \neg E)$, then is $P(A) > P(B)$ true?
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
70552
Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime