gcd (a,b)

JoeSal

New member
Joined
Apr 20, 2007
Messages
12
Hi,

The following problem is:

If gcd(a,b)=1 AND a|c AND b|c THEN prove ab|c.

From this I can conclude:

a,b are relatively prime
****there are no commons factors of a,b other than 1.
lcm(a,b)=a*b...but I this may not be relevant.
****c is a common facter of a,b.

The problem also mentions:

there exists two integers x,y such that xa +ya=1. I am confused about this statement an haven't implemented it into my solution.

The only thing I can come up with is that if gcd(a,b)=1 then 1 is the only divisor of both a,b and also, c is a divisor of both a,b. therefore, c=1. and ab is divisible by 1.

But this appears too easy..

Any other suggestions?
 
Sorry, the statement below should be:

there exists two integers x,y such that xa +yb=1
 
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