Problem
NT-B2-M03-P003 A Power Modulo Seven
#3
★★☆☆☆ Level 2 of 5
Find the remainder of \(2^{100}\) modulo \(7\).
Use \(2^3\equiv1\pmod7\).
Since the order of \(2\) modulo \(7\) is \(3\), reduce the exponent: \(100\equiv1\pmod3\). Hence \(2^{100}\equiv2\pmod7\).
Distinguishes cycle computation from blindly applying Fermat's theorem.