Problem
NT-B2-M04-P012 Euler or CRT
#12
★★★★☆ Level 4 of 5
Find the remainder of \(7^{222}\) modulo \(100\).
Use \(\varphi(100)=40\), but a short cycle is even better.
Notice that \(7^4\equiv1\pmod{100}\). Since \(222\equiv2\pmod4\), we get \(7^{222}\equiv7^2=49\pmod{100}\).
Discuss that Euler gives a valid but not always shortest reduction.