Problem
NT-B1-M07-P010 A Power of \(-1\)
#10
★★☆☆☆ Level 2 of 5
Find the remainder of \(11^{2025}\) modulo \(12\).
Notice that \(11\equiv-1\pmod{12}\).
\(11\equiv-1\pmod{12}\). The exponent \(2025\) is odd, so \(11^{2025}\equiv(-1)^{2025}\equiv-1\equiv11\pmod{12}\).
Sometimes the best replacement is \(-1\).