True or false If true give a proof if false give a counter e

True or false? If true give a proof, if false give a counter example. For all a Z+, if a > 3 then a^24 is composite.

Solution

given that a>3.

Then a²-4 is a composite number.

Proof:

a²-4 = a²-2² which is equal to (a+2)(a-2) [ since a²-b² = (a+b) (a-b) ]

hence a²-4 = (a+2)(a-2) which is a composite number as it can be written as a multiplication of 2 numbers.