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There are several ways to prove a mathematical statement. These ways include: by contradiction, by induction, contraposition, etc
<h3>How to prove the statement by contradiction</h3>To prove the statement, we make use of proof by contradiction
From the question:
x is a composite number such that: x > 1
This means that 1 < a < x is a factor of x
This can be represented as:
Where:
- a and b are positive integers
- 1 < a, b < x
Assume that b is less than or equal to a.
Also, let
This means that:
The above becomes
Rewrite as:
So, we have:
The above means that:
The above inequality is a contradiction because, a number x cannot be greater than itself
This means that, the supposition is wrong.
Hence, the given statement has been proved by contradiction
Read more about proof by contradiction at: