Problem
NT-B1-M03-P020 Last Two Digits
#20
★★★☆☆ Level 3 of 5
Find the last two digits of \(3^{20}\).
Work modulo \(100\). Notice that \(3^4=81\).
\(3^{20}=(3^4)^5=81^5\). Modulo \(100\): \(81^2\equiv61\), \(81^4\equiv61^2\equiv21\), \(81^5\equiv21\cdot81\equiv1\). Therefore the last two digits are \(01\).
Shows the difference between the last digit and the last two digits.