Problem
NT-B2-M04-P008 Last Two Digits
#8
★★★☆☆ Level 3 of 5
Find the last two digits of \(3^{80}\).
Work modulo \(100\).
\(\gcd(3,100)=1\), \(\varphi(100)=40\). Euler gives \(3^{40}\equiv1\pmod{100}\), hence \(3^{80}\equiv1\pmod{100}\). The last two digits are \(01\).
Show why modulus \(100\) calls for Euler or CRT.