Help with the Euclidian Theorum: "If a|bc and gcd(a,b)=1, then a|c"

[Red_Rocket]

Hey there!

I'm trying to understand what i'm missing about this proof:

Prove that if a|bc and gcd(a,b)=1, then a|c

 

[stapel]

I'm trying to understand what i'm missing about this proof:

Prove that if a|bc and gcd(a,b)=1, then a|c

Do you mean that you've been given a proof, and you don't understand some portion of it? If so, please post that proof and specify the portions which are confusing to you.

Or do you mean that you need to do the proof yourself, and are getting stuck? If so, please post what you've tried so far, so we can see where you're bogging down.

Please be complete. Thank you!

 

[Steven G]

Hey there!

I'm trying to understand what i'm missing about this proof:

Prove that if a|bc and gcd(a,b)=1, then a|c

To write a proof or even to understand a proof you need to know the definitions
What does a|bc mean?
What does gcd(a,b)=1 mean?
How about a|c?

How does having the 1st two give the third?

Think