**Theorem: Let p be a prime number. If p divides , then p divides a, where a is a positive integer.**

**Solution:**

Let where, p1, p2, p3, ..., pn are prime numbers which are necessarily not distinct.

It is given that **p** divides . From the **Fundamental theorem of Arithmetic**, we know that every composite number can be expressed as product of unique prime numbers. This means that **p **is one of the numbers from (p1.p2.p3.p4.p5......pn).

We have **a=(p1.p2.p3.p4.p5..pn)** and **p** is one of the numbers from (p1.p2.p3.p4.p5......pn).

It means that **p** also divides **a.**

Hence, it is proved that if **p **divides then it also divides **a.**