CBSE Class 10 Answered

We know by the Fundamental Thm of Arithmetic that

every composite number canbe factorised in a unique way as a product of prime numbers.

Consider a as the product of prime numbers

Now, the Fundamental Theorem  tells us that since p divides a squared, so p must be one of the prime factors of a squared. But from the 'unique' factorisation part of the theorem we can say that the only prime factors of a squares are p1, p2, p3... pn.

So p must be one of these numbers.

Since a is the product of these numbersp1,p2..pn, so p must  divide a.This proves it.

You can try this by giving values to a and p and check it. It will help you understand it even better.