Problem
NT-B2-M06-P018 When \(7^n\) Divides
#18
★★★★★ Level 5 of 5
Find all positive integers \(n\) such that \(7^n\mid8^n-1\).
Use \(v_7(8^n-1)=1+v_7(n)\).
We need \(1+v_7(n)\ge n\). For \(n=1\), the condition holds. If \(n\ge2\), then \(v_7(n)\le \log_7 n
Similar idea, but with stricter growth.