Al(bc), then either alb or alc

[kathrynag]

Homework Statement

al(bc), then either alb or alc
I'm trying to explain why this is true.

Homework Equations

The Attempt at a Solution

a divides bc.
a divides b or a divides c is true because b is just a multiple of c and a will still be a factor.

 

[VeeEight]

This statement is true only if a is prime. Use the fact that if gcd (a,b) = c then there is some integers x,y such that ax+by=c

 

[Mark44]

It's not true. Counterexample: 4 | 12, but 4 doesn't divide 6 and 4 doesn't divide 2.