Problem
NT-B2-M03-P004 Last Digit
#4
★★☆☆☆ Level 2 of 5
Find the last digit of \(3^{2026}\).
Work modulo \(10\); the powers of \(3\) have cycle length \(4\).
Powers of \(3\) modulo \(10\) are \(3,9,7,1\), then the cycle repeats. Since \(2026\equiv2\pmod4\), the last digit is \(9\).
The modulus is composite, but the base is coprime to \(10\).