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【OG20-P177-200题】
If n = (33)43 + (43)33, what is the units digit of n ?
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分析A选项
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分析B选项
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分析C选项
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分析D选项
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分析E选项
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借我借我一双慧眼吧 更新于2015-11-27 17:45:40 感谢由
借我借我一双慧眼吧 对此题目的解答所做出的贡献。
幂指数的考题
33和43的次方数，各位数字应该是3.9.7.1
43/4=10...3 第三位，那就是7
33/4=8...1 第一位：3
所以是相加为10 所以各位为0
题目讨论 （3条评论）
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emily666
懂了，四个数循环，刚好个位数分别是7，3
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2020-03-12 23:27:08
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黑猫警长
转自 GMATclub irst of all, the units digit of (33)^43 is the same as that of 3^43 and the units digit of (43)^33 is the same as that of 3^33. So, we need to find the units digit of 3^43 + 3^33. Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}: 3^1=3 (the units digit is 3) 3^2=9 (the units digit is 9) 3^3=27 (the units digit is 7) 3^4=81 (the units digit is 1) 3^5=243 (the units digit is 3 again!) ... Thus: The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3). The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1). Therefore the units digit of (33)^43 + (43)^33 is 7 + 3 = 0.0
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2019-07-10 21:44:24
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默默
看末位数的循环
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2018-04-28 06:40:15
