Problem
NT-B2-M03-P005 Order Through \(-1\)
#5
★★☆☆☆ Level 2 of 5
Find \( \operatorname{ord}_{13}(5) \).
Notice that \(5^2\equiv-1\pmod{13}\).
\(5^2=25\equiv12\equiv-1\pmod{13}\). Hence \(5^4\equiv1\). The order is not \(1\) or \(2\), because \(5\not\equiv1\) and \(5^2\not\equiv1\). Therefore the order is \(4\).
A useful template for \(a^2\equiv-1\).