Answer:
Proof given by contradiction.
Explanation:
Given that:

To prove:
is prime if and only if no positive integer > 1 and
divides
.
Solution:
First of all, let
is a composite number i.e. not a prime number such that:

and
and
are prime and
divides
and
also divides
.
Let

or

1.
:
is prime and is a divisor of
.
2.
:

We have assumed that

is a prime number and is a divisor of
.
But we are given that no prime number
divides
but we have proved that
divides
.
So, it is a contradiction to our assumption.
Therefore, our assumption is wrong that
is a composite number.
Hence, proved that
is a prime number.