Question

prove that two consective positive integers are always coprime​

Answer 1

Answer:

Let two consecutive numbers are n and n+1.

Assume they are not co-primes.

Then gcd(n,n+1)=x, because it can not equal to 1, x is natural and x>1

So x divides n as well as n+1.

Then x also divides n+1−n, by general understanding.

Hence x divides 1 or x=1.

But we have assumed x>1.

So by contradiction n & n+1 are co-prime.

Is it right or is there any better way to prove that two consecutive numbers are co-prime?