$a,b \in Z$ and $p$ is prime. If $p|ab$ then $p|a$ or $p|b$
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
17677
Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
46286
Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers.
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
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 $p$.
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
20881
Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
36043
If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
58935
If $p$ and $p^2+8$ are both prime numbers, then $p^3+4$ is prime.
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?