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