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Decimal Digit Determination (Posted on 2013-08-24) Difficulty: 3 of 5
Determine the digit immediately to the left of the decimal point in the base ten representation of (3+√7)2004

**** For an extra challenge, solve this puzzle using only pen and paper.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re(2): much of a problem even with a computer | Comment 4 of 5 |
(In reply to re: much of a problem even with a computer by broll)

No idea.

However, there may be a recurrence such that y = (3-sqrt(7))^(24n+m)+(3+sqrt(7))^(24n+m) has the same final digit for all {m, n}; though I certainly haven't attempted an exhaustive check.

If so, since 2004 = 24*83+12, it will have the same last digit as y = (3-sqrt(7))^(12)+(3+sqrt(7))^(12)  - a more manageable 1048723328.

Still a stretch for P&P though.

  Posted by broll on 2013-08-25 12:36:13
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