Problem
NT-B2-M06-P006 The Condition \(7^3\)
#6
★★★☆☆ Level 3 of 5
Find all positive integers \(n\) such that \(7^3\mid8^n-1\).
Compute \(v_7(8^n-1)\).
\(v_7(8^n-1)=1+v_7(n)\). We need \(1+v_7(n)\ge3\), i.e. \(v_7(n)\ge2\). Answer: all \(n\) divisible by \(49\).
Good transition from computation to solution sets.