Composite Number
An integer \(n > 1\) is called a composite number if it is not a prime number.
Any composite number has a non-trivial factorisation.
For any \(n > 1\) composite, there exists integers \(a, b\) satisfying \(1 < a, b < n\) such that \(ab = n\).
Proof
If \(n\) is composite, then it is not prime, and since \(1 \mid n\) and \(n \mid n\) always, this means there is another non-trivial divisor of \(n\), which we denote by \(a\). We can assume \(a > 0\) because we can simply adjust the sign of the other divisor appropriately.
Clearly if \(a \geq n\), then \(ab \geq n\) for any positive integer \(b\). Therefore given \(a \neq 1\) and \(a \neq n\), we have that \(1 < a < n\).
Similarly if \(b\) is such that \(ab = n\), which exists because \(a \mid n\), then \(1 < b < n\) because if \(b \geq n\) then \(ab \geq n\).
Hence we have \(n = ab\) for \(1 < a, b < n\).