AMC 8 2000 Problem 14
AMC8 2000 年第 14 题
余数与同余★★★☆☆
What is the units digit of ?
的个位数字是多少？
- A.0
- B.1
- C.2
- D.8
- E.9
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Finding a pattern for each half of the sum, even powers of 19 have a units digit of 1, and odd powers of 19 have a units digit of 9. So, has a units digit of 9. Powers of 99 have the exact same property, so also has a units digit of 9. 9+9=18 which has a units digit of 8, so the answer is .
Using modular arithmetic: Similarly, We have -ryjs
Experimentation gives Using this we have Both 19 and 99 are odd, so we are left with 9+9=18, which has units digit -ryjs
36972963764972677265718790562880544059566876428174110243025997242355257045527752342141065001012823272794097888 9548326540119429996769494359451621570193644014418071060667659303363419435659472789623878 which ends in 8.:) If you are really stupid and have time (like about 3 hours), this is a real brainless bash.
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