Problem
NT-B2-M04-P002 A Power Modulo \(9\)
#2
★★☆☆☆ Level 2 of 5
Find \(2^{100}\pmod9\).
Use \(\varphi(9)=6\).
Since \(\gcd(2,9)=1\), Euler gives \(2^6\equiv1\pmod9\). Since \(100\equiv4\pmod6\), \(2^{100}\equiv2^4=16\equiv7\pmod9\).
Coprimality must be checked.