Problem
NT-B1-M07-P007 A Power of Two Modulo \(13\)
#7
★★☆☆☆ Level 2 of 5
Find the remainder of \(2^{100}\) modulo \(13\).
Use \(2^{12}\equiv1\pmod{13}\).
By Fermat, \(2^{12}\equiv1\pmod{13}\). Since \(100\equiv4\pmod{12}\), \(2^{100}\equiv2^4=16\equiv3\pmod{13}\).
Standard exponent-reduction problem.