Prove if a b c are integers and p is prime such that pa and

Prove if a, b, c are integers and p is prime such that p|a and p|(a + bc), then p|b or p|c.

| = divides

Solution

p|a means

a=mp where m is some integer

p|(a+bc) means

a+bc=np where n is some integer

So, bc=(n-m)p

Hence, p|bc

SInce p is prime number

Hence, p|b or p|c