Problem
NT-B1-M11-P002 Consecutive Numbers
#2
★☆☆☆☆ Level 1 of 5
Prove that \(\gcd(n,n+1)=1\).
A common divisor divides the difference.
If \(d\mid n\) and \(d\mid n+1\), then \(d\mid (n+1)-n=1\). Thus \(d=1\), so the GCD is \(1\).
Mini-lemma often used implicitly.