Problem
NT-B2-M06-P007 A Power of \(9\)
#7
★★★☆☆ Level 3 of 5
Find the largest \(k\) such that \(9^k\mid10^{2025}-1\).
First find \(v_3\).
From Problem 1, \(v_3(10^{2025}-1)=6\). Since \(9^k=3^{2k}\), \(2k\le6\), hence \(k=3\).
Checks work with a composite base.