Question

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

Answer 1

Answer:

Step-by-step explanation:

(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 at least divisible by 2.  

 

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

hope this helps :)