Problem
NT-B1-M12-P011 Set 2. Last Two Digits
#11
★★☆☆☆ Level 2 of 5
Find the last two digits of \(11^{2025}\).
Check the pattern of \(11^k\pmod{100}\).
For \(k=1,\ldots,10\), we get \(11,21,31,\ldots,91,01\), a cycle of length \(10\). Since \(2025\equiv5\pmod{10}\), the last two digits are \(51\).
Good task on two-digit notation in a cycle.