# Thread: Applying Euclid's Lemma to a problem

1. ## Applying Euclid's Lemma to a problem

Hello there,

I have a problem that i have troubles starting. I need to show if gcd(a, c)=1 and c divides ab, then c divides (ab + bx). My prof gave us a hint to use Euclid's lemma, which states if a divides bc and gcd(a, b) = 1 then a divides c.

Edit: Ok, so i figured that, from Euclid's lemma we can get that c divides b, but now im stuck again

Thank you in advance.

2. ## Re: Applying Euclid's Lemma to a problem

if you've realized that c divides b, can you factor b out of your expression?

3. ## Re: Applying Euclid's Lemma to a problem

Wow.. i was looking for some hard trick.. it's so simple.. i feel like a fool heh..
Thank you very much!

God Bless!

4. ## Re: Applying Euclid's Lemma to a problem

oklets firstlyy c/ab & gcd(a.c)=1 so c/b then c/bx & c/ab
finally c divise any linear combinaison between ab and bx
so c/ab+cx ..