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Divisible by 7 (Posted on 2007-02-15) Difficulty: 3 of 5
Prove that if A = ½(15+√197), then 7 is a factor of [A^n] for all positive integer values of n, where [w] denotes the greatest integer less than or equal to w.

See The Solution Submitted by Dennis    
Rating: 4.0000 (1 votes)

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Hints/Tips re(3): Look for the conjugate | Comment 4 of 5 |
You're on the right track Ady, but need to show that the SUM A^n + B^n = 7k+1 where k is a positive integer.
  Posted by Dennis on 2007-02-26 12:14:00
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