Prove that if a|b, c|d, then ac|bd
39953
$a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
152693
If $C|a$ and $C|b$ then $C|(ax+by)$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
31724
How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
100571
Prove $(1-a)(1-b)(1-c)(1-d)\geq abcd$ if $a^2+b^2+c^2+d^2=1$
66563
Is $ (A∪B)×(C∩D)=(A∪C)×(B∪D)$ true for all sets A,B,C and D?
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
111800
If $a|c$ and $b|d$, is it true that $ab|cd$?
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
124742
P(A|C)=P(A|B)*P(B|C)?
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
39621
Let a, b, c, d be rational numbers...
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
32253
How to prove $b=c$ if $ab=ac$ (cancellation law in groups)?