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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.)
re: computer exploration | Comment 2 of 5 |
(In reply to computer exploration by Charlie)

I noticed the last numbers on each line get larger by a factor of about 13.9 each time, so I ran a similar program to investigate this more and found this factor converging to some limit -- I wonder what it is exactly?  Here is the output of my program:

8             13            13
105           181           13.9230769
1456          2521          13.9281768
20273         35113         13.9282031
282360        489061        13.9282032
3932761       6811741       13.9282032

  Posted by Jim Keneipp on 2010-02-27 18:20:40
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