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Last Digit (Posted on 2004-01-23) Difficulty: 3 of 5
Find the last digit of summation of the series:
(1)^99 + (2)^99 + (3)^99 + (4)^99 + + (98)^99 + (99)^99

See The Solution Submitted by Ravi Raja    
Rating: 2.4000 (5 votes)

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SOLUTION | Comment 2 of 19 |
It must be zero, since whatever result is achieved from the summation of the first ten members (actually it is 5 but that is irrelevant) is then repeated nine more times so we have summation of this digit 10 times .

Remark(NOT NEEDED TO SOLVE THE PUZZLE): the last digit of Nth power of any number is equal to the last digit of Kth power of said number iff(=if and only if) M mod 4= N mod 4 i.e. consider the 3th power instead of the 99th.

Edited on January 23, 2004, 10:29 am
  Posted by Ady TZIDON on 2004-01-23 09:57:59
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