Problem
NT-B1-M11-P018 Ones and Divisibility by \(7\)
#18
★★★☆☆ Level 3 of 5
Find all \(n\) for which \(7\mid R_n\).
The condition is equivalent to \(10^n\equiv1\pmod7\).
Since \(9\) is invertible modulo \(7\), \(7\mid R_n\) exactly when \(10^n\equiv1\pmod7\). The order of \(10\equiv3\) modulo \(7\) is \(6\). Therefore precisely the multiples of \(6\) work.
Revisits order in a mixed context.