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Seven powers of seven (Posted on 2006-09-08) Difficulty: 2 of 5
1. What is the last digit of 7777777 = 7^(7^(7^(7^(7^(7^7))))) ?

2. More generally, if we define the hyper power na by

1a:=a, n+1a:=a(na) for n>=1

does the series of the last digits of 1a, 2a, 3a,... always become periodic at some point?

If so, can you provide a sharp upper limit for the period length?

Note: The hyper power na is also often denoted as a^^n.

See The Solution Submitted by JLo    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
For the first part..... Comment 3 of 3 |
... the required last digit is 3
  Posted by K Sengupta on 2008-08-21 07:18:55
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