Question

if a and b are two odd number show that (α2-b2) is composite​

Answer 1

Answer:

let a=5 and b=3

=(2×5-2×3)

=(10-6)

=4.

Showed that 2a-2b =4

Answer 2

Answer:

(a^2-b^2) = (a-b)(a+b)

Now, a and b are 2 odd prime numbers and the difference of 2 odd numbers is an even number. Also, the sum of 2 odd numbers is always even.

Hence, (a-b) and (a+b) are both even numbers and hence are atleast divisble by 2.

So, 2 is a factor of (a^2-b^2) and hence (a^2-b^2) is a composite number.