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I want to find the unit digit of $ 1^1+2^2+3^3+...+2018^{2018} $ . I have find out the unit digit of $ 2^2,3^3,4^4,....259^{259},....2018^{2018}$ . But I cant find out the unit digit of sum of all of this term .

Is there any way to find out the digit of sum of all of this term ? Please help me .

Jyrki Lahtonen
  • 133,153
Christopher Marlowe
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  • Hint: The final unit digit depends only on the unit digit of each value. With each value, this depends only on the final digit of each integer. If you try some of these, you should notice a pattern which you can use to simplify your calculations. – John Omielan Dec 25 '18 at 05:59
  • I have find out unit digit of each term . Then what can I do ? – Christopher Marlowe Dec 25 '18 at 06:00
  • Hint #2: If you take each unit digit to increasing powers, just checking the unit digit each time, you will see the values start repeating after a while. – John Omielan Dec 25 '18 at 06:02

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