Problem
NT-B1-M11-P007 GCD of Expressions
#7
★★☆☆☆ Level 2 of 5
Find \(\gcd(n^2-1,n+1)\) for positive integer \(n\).
Factor \(n^2-1\).
Since \(n^2-1=(n-1)(n+1)\), the number \(n+1\) divides \(n^2-1\). Therefore \(\gcd(n^2-1,n+1)=n+1\).
Easy but important link between GCD and divisibility.