Question

If $a$ and $b$ are two odd prime numbers, show that $a^2-b^2$ is composite.

Answer 1

$a^2-b^2$ $=(a+b)(a-b)$ {standard algebraic Identity}

It is given that, $a$, $b$ are two odd primes.

$\Rightarrow (a+b),(a-b)$ is an even numbers

Since $(a+b)$ and $(a-b)$ are factors, therefore, the number is a composite number.