For all integers a, b, c, if a | b and b | c then a | c.
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
21006
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
30261
How can I find all integers $x≠3$ such that $x−3|x^3−3$
132971
Prove that $|a| < b \iff -b<a<b$
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
58579
Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
124320
$a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
127296
prove that a|b and b|a iff a=+-b
54699
Product of pairwise coprime integers divides $b$ if each integer divides $b$
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
92290
For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive