Therefore, the hundreds digit is (D)6. Sidenote: By Euler's Totient Theorem, aϕ(1000)≡a(mod1000) for any a, so a400≡a(mod1000) and 112011≡1111(mod1000). We can then proceed using the clever application of the Binomial Theorem. We need to compute 20112011(mod1000). By the Ch...
What is the hundreds digit of 20112011?( ) 20112011 百位上的数字是多少?( ) A.1 B.4 C.5 D.6 E.9相关知识点: 试题来源: 解析 D Since 2011≡11(mod 1000), we know that 20112011≡112011(mod 1000). To compute this, we use a clever application of the binomial theorem. 112011=(1+10...
Therefore, the hundreds digit is (D)6. Sidenote: By Euler's Totient Theorem, aϕ(1000)≡a(mod1000) for any a, so a400≡a(mod1000) and 112011≡1111(mod1000). We can then proceed using the clever application of the Binomial Theorem. We need to compute 20112011(mod1000). By the Ch...
百度试题 结果1 题目What is the hundreds digit of 20112011?( )(2011 AMC 10B Problem, Question #23) A.1 B.4 C.5 D.6 E.9 相关知识点: 试题来源: 解析 D 反馈 收藏