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Sum Of The Digits (Posted on 2004-01-27) Difficulty: 3 of 5
Find sum of digits of:(1999)^1999.
[The final answer should be a single digit number, for example, (2)^16 = 65536 and the sum of its digits will be given by (6 + 5 + 5 + 3 + 6 = 25, which again will be reduced to 2 + 5 = 7].

See The Solution Submitted by Ravi Raja    
Rating: 2.1667 (6 votes)

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Solution re(2): super easy | Comment 4 of 13 |
(In reply to re: super easy by SilverKnight)

Adding the digits of a number, is the same as calculating the residue of dividing it by 9. So, asking for the sum of digits of 1999^1999 is the same as asking for

(1999^1999) mod 9 =

(1999 mod 9)^1999 mod 9 =

1^1999 mod 9 = 1

  Posted by e.g. on 2004-01-27 09:11:38

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