Problem
NT-B2-M04-P009 Incomplete Factorial
#9
★★★☆☆ Level 3 of 5
Find \(8!\pmod{11}\).
Express \(10!\) through \(8!\).
By Wilson, \(10!\equiv-1\pmod{11}\). But \(10!=10\cdot9\cdot8!\equiv(-1)(-2)8!\equiv2\cdot8!\). Hence \(2\cdot8!\equiv10\), so \(8!\equiv5\pmod{11}\).
Classic trick: remove the last factors.