Problem
NT-B2-M04-P001 A Power Modulo \(11\)
#1
★★☆☆☆ Level 2 of 5
Find \(2^{2026}\pmod{11}\).
Reduce the exponent modulo \(10\).
By Fermat, \(2^{10}\equiv1\pmod{11}\). Since \(2026\equiv6\pmod{10}\), we get \(2^{2026}\equiv2^6=64\equiv9\pmod{11}\).
Basic direct application of Fermat.