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The Last Two Digits (Posted on 2013-09-04) Difficulty: 2 of 5
What are the last two digits of (1+5^(2n+1))/6?
Note that n is assumed to be any positive integer.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (1 votes)

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another way | Comment 2 of 3 |
Factor the numerator as (1+5)(1-5+...+5^2n) and note that positive powers ending in 25 are offset by negatives.  You're left with (1-5+25)=21 since the (1+5) factor cancels.  
  Posted by xdog on 2013-09-04 12:22:43
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