Problem
NT-B2-M01-P016 Mixed Exponents
#16
★★★★☆ Level 4 of 5
Find \( \gcd(4^m-1,2^n-1) \) in terms of \(m\) and \(n\).
Replace \(4^m-1\) by \(2^{2m}-1\).
Since \(4^m-1=2^{2m}-1\), the power formula gives \( \gcd(2^{2m}-1,2^n-1)=2^{\gcd(2m,n)}-1 \). This is the answer.
The problem is short, but it teaches students to first bring the bases to one form.