Prove that if $a \mid b$ and $b \mid c$ then $a \mid (bx +cy)$ for all $a,b,c,x,y \in \mathbb{N}$
56512
Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
39175
Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
21241
Proving $\,a\mid bc\!\iff\! \frac{a}{(a,b)}\!\mid c\ $ [general Euclid's Lemma]
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
152693
If $C|a$ and $C|b$ then $C|(ax+by)$
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $