Problem
NT-B2-M06-P013 Criterion Through \(n\)
#13
★★★★☆ Level 4 of 5
Find all \(n\) such that \(3^5\mid4^n-1\).
Use \(v_3(4^n-1)=1+v_3(n)\).
We need \(1+v_3(n)\ge5\), i.e. \(v_3(n)\ge4\). Answer: \(81\mid n\).
Short but good translation of prime-power divisibility.