Question

a ,b are natural numbers given that a^2-b^2 is prime. Prove that a+b is prime

Answer 1

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

Given that a^2-b^2 is prime and that a and b are natural numbers
(i.e. \[a, b \in Integer^+ \], then we can say that a-b = 1 and (a+b)=(a^2-b^2), so a+b is also prime (Proven).