A couple of questions I'm confused about

Apr 2016
3
0
London
The following are a couple of questions that I'm getting a bit confused as to how to answer them, any help is appreciated.

1)
AcroRd32_2016-04-05_22-23-47.png

2)
AcroRd32_2016-04-05_22-24-01.png
 
Dec 2013
2,002
757
Colombia
1) write a=dp and b=dq. Show that dp divides (ab)/d and that dq also divides (ab)/d.
2) m=ac=bd. Since l=lcd(a,b) divides a and l divides b we get m=lcp=ldq=lk and so l divides m.
 
Last edited:
Apr 2016
3
0
London
How do you show that dp and dq divides (ab)/d? (Thanks for your help for the second one though, I understood that pretty easily)
 

romsek

MHF Helper
Nov 2013
6,836
3,079
California
How do you show that dp and dq divides (ab)/d? (Thanks for your help for the second one though, I understood that pretty easily)
$a = pd$, $b=qd$

$\dfrac {ab}{d} = \dfrac{pq d^2}{d} = pqd$

$pqd=(pd)q = aq$

$pqd = p(qd) = pb$

and thus $\dfrac{ab}{d}$ is a multiple of both $a$ and $b$