Question

show that if a|bcd and (a,b)=(c,d)=1, then a|d

Answer 1

@tcarroll010 this is the one I was referring to..

Answer 2

the "|" is the symbol for divides... fyi

Answer 3

@tcarroll010 correct me if I am wrong.

Answer 4

b and c do not equal one, but the GCD is one meaning they are relatively prime

Answer 5

(a,b) is notation for GCD

Answer 6

No discard my comment. HA

Answer 7

I AM TOTALY WRONG I AM SO SORRY

Answer 8

its ok, thanks for at least trying!!!

Answer 9

@amistre64 @satellite73

Answer 10

yes

Answer 11

@amistre64 @satellite73

Answer 12

I think there is a mistype ! I think it should be (a,b)=(a,c)=1.
If it is the case, then the respond will be like this :


Because (a,b)=1 Then :
\[an+bm=1\quad \quad \quad (1)\]
where n and m are integers !
The same thing, because (a,c)=1 Then :
\[au+cv=1\quad \quad \quad (2)\]
where u and v are integers !
And because a|bcd then :
\[bcd=ka\quad \quad \quad (3)\]
By multiplying the equation (1) by cd we get :
\[ancd+cbdm=cd\]
From (3) we get :
\[ancd+ka=cd\]
that means :
\[a(ncd+k)=cd\]
And then :
\[a|cd\]
By the same method above we get :
\[a|d\]

Answer 13

you are right... THANK YOU!! @Noura11