20112011=(2011100)20⋅201111 ≡120⋅1111 =1215⋅11 =(−4)5⋅11=−1024⋅1 ≡−24⋅11=−264 ≡111(mod 125). After finding the solution 20112011≡611(mod 1000), we conclude it is the only one by the Chin