Problem
NT-B2-M04-P007 Power Remainder
#7
★★★☆☆ Level 3 of 5
Find \(7^{100}\pmod{13}\).
Reduce the exponent modulo \(12\).
By Fermat, \(7^{12}\equiv1\pmod{13}\). Since \(100\equiv4\pmod{12}\), \(7^{100}\equiv7^4\). Now \(7^2=49\equiv10\), so \(7^4\equiv100\equiv9\pmod{13}\).
Standard two-step task: reduce exponent and compute.