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Little cubes (Posted on 2010-02-27) Difficulty: 4 of 5
The difference of the cubes of two non-negative successive integers is a square of an integer. Find few possible pairs.
How about a general formula or evaluation algorithm for a(n)?

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(2): computer exploration | Comment 3 of 5 |
(In reply to re: computer exploration by Jim Keneipp)

I noticed that too.  That near-geometric increase comes from the recursion t(n) = 14*t(n-1) - t(n-2), with starting values t(0)=1, t(1)=13.  Taking x^2 = 14x - 1, then x = 7 +/- 4*sqrt[3].  The larger root evaluates to 13.92820322.

Edited on February 27, 2010, 6:56 pm
  Posted by Brian Smith on 2010-02-27 18:51:49

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