Question

if a and b are two odd numbers , show that a2-b2 is composite​

Answer 1

Before the answer we have to make out what a composite number means. It is an integer which can be written as the product of two distinct integers which are neither 1 nor the integer itself.

Let there exists two distinct odd numbers a and b, as mentioned in the question. Then what about a² - b²?

a² - b² = (a + b)(a - b)

Thus it can be written as the product of two integers a + b and a - b. But, can these numbers be either 1 or the number a² - b² itself?

Reason is that, since a and b are odds, then both a + b and a - b are even numbers, so that none of them can't be 1, which is odd. Then what about either a + b or a - b being equal to a² - b²?!