Problem
NT-B1-M02-P016 GCD of Two Mersenne-Type Numbers
#16
★★★☆☆ Level 3 of 5
Find \(\gcd(2^{18}-1,2^{30}-1)\).
Use \(\gcd(18,30)=6\).
For numbers of the form \(a^m-1\), \(\gcd(a^m-1,a^n-1)=a^{\gcd(m,n)}-1\). Hence the required GCD is \(2^6-1=63\).
Can be assigned after the formula is discussed in examples or before the general proof.