Let p be a prime number and b c in Z such that 0

Let p be a prime number, and b, c in Z such that 0<b, c<p.
                Prove that p does not divide bc.

Solution

Solution :

Since b and c is less than p.

This implies.

p does not divide b and p does not divide c.

If p divides bc then p being prime must divide either b or c which is contradiction.

Therefore, p does not divide bc.