Problem
NT-B1-M02-P005 GCD with a Linear Expression
#5
★☆☆☆☆ Level 1 of 5
Prove that \(\gcd(n,2n+1)=1\) for every integer \(n\).
Subtract \(2n\) from \(2n+1\).
Any common divisor \(d\) of \(n\) and \(2n+1\) divides \(2n\), hence divides \((2n+1)-2n=1\). Therefore \(d=1\), so the GCD is \(1\).
First use of a linear combination.