Prove the following facts about relative primality 1.Two consecutive integers (n and n + 1) are always relatively prime. 2.Two consecutive Fibonacci numbers are always relatively prime. 3. Two...

Prove the following facts about relative primality

1.Two consecutive integers (n and n + 1) are always relatively prime.

2.Two consecutive Fibonacci numbers are always relatively prime.

3. Two integers a and b are relatively prime if and only if there is no prime number p such that p | a and p | b. (Notice that this claim differs from the definition of relative primality, which required that there be no integer n ≥ 2 such that n | a and n | b.)