Problem
NT-B2-M06-P011 General Form for \(5^n-1\)
#11
★★★★☆ Level 4 of 5
Find \(v_2(5^n-1)\) depending on the parity of \(n\).
For odd \(n\), use the \(5-1\) factor; for even \(n\), use the formula for \(2\).
If \(n\) is odd, \(v_2(5^n-1)=v_2(5-1)=2\). If \(n\) is even, \(v_2(5^n-1)=v_2(4)+v_2(6)+v_2(n)-1=2+1+v_2(n)-1=2+v_2(n)\).
Requires a careful case split.