Problem
NT-B1-M02-P004 Consecutive Numbers
#4
★☆☆☆☆ Level 1 of 5
Prove that \(\gcd(n,n+1)=1\) for every integer \(n\).
A common divisor divides the difference.
If \(d\mid n\) and \(d\mid n+1\), then \(d\mid(n+1)-n=1\). Hence \(d=1\). Therefore \(\gcd(n,n+1)=1\).
Short template: a common divisor divides any difference.