Problem
NT-B1-M07-P008 A Power of Seven Modulo \(9\)
#8
★★☆☆☆ Level 2 of 5
Find the remainder of \(7^{50}\) modulo \(9\).
Check \(7^3\) modulo \(9\).
\(7^2=49\equiv4\pmod9\), \(7^3\equiv4\cdot7=28\equiv1\pmod9\). Since \(50\equiv2\pmod3\), \(7^{50}\equiv7^2\equiv4\pmod9\).
Here the short cycle has length \(3\).