Prove that if a and b are positive integers whose sum is a prime p, their greatest common divisor is 1.

Proof by contadiction.

Let assume there exist such positive integers and whose sum is a prime number , that their greatest common divisor is greater than 1.

Since is a prime number and , then , but we assumed earlier that , and there are no two positive integers that sum up to 1.

q.e.d.

b. astronomers