Problem
NT-B1-M07-P009 Last Two Digits of \(3^{40}\)
#9
★★☆☆☆ Level 2 of 5
Find the last two digits of \(3^{40}\).
Work modulo \(100\) and apply Euler's theorem.
\(\gcd(3,100)=1\), and \(\varphi(100)=40\). By Euler's theorem, \(3^{40}\equiv1\pmod{100}\). Thus the last two digits are \(01\).
Good first use of Euler for \(100\).