Problem
NT-B1-M07-P001 Cycle of Powers of Two
#1
★☆☆☆☆ Level 1 of 5
Find the remainder of \(2^{17}\) modulo \(5\).
List the first four powers of \(2\) modulo \(5\).
We get \(2,4,3,1\), then the cycle repeats with period \(4\). Since \(17\equiv1\pmod4\), \(2^{17}\equiv2\pmod5\).
Basic problem on residue cycles.