Question

Prove that any two consecutive integers are relatively prime​

Answer 1

It is false as we may take 2 of them

3 and 4

3 is prime but 4 is not

It shows it is false

Answer 2

Answer:

Problem 11.38a Prove that every two consecutive odd positive integers are relatively prime. Solution: Let 2n − 1 and 2n + 1 be our two consecutive odd positive integers, and let d | 2n − 1, d | 2n + 1. Thus d = 1 or d = 2. ... Thus the only divisor of 2n − 1 and 2n + 1 is 1, and so they are relatively prime as claimed.