perplexus.info :: Numbers : Little cubes

Little cubes (Posted on 2010-02-27)

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)?

Submitted by Ady TZIDON

Rating: 4.0000 (2 votes)

Solution: (Hide)

Some couples (a,b) for (a+1)^3-a^3=b^2 :
(0, 1), (7, 13), (104, 181),...
To get more, use the recurrence relations :
a[n] = 14a[n-1] - a[n-2] + 6 and b[n] = 14b[n-1] - b[n-2]

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: computer exploration -- Sloane back on-line	Charlie	2010-03-01 03:02:49
Analytical findings (spoiler)	Harry	2010-02-27 21:14:12
re(2): computer exploration	Brian Smith	2010-02-27 18:51:49
re: computer exploration	Jim Keneipp	2010-02-27 18:20:40
computer exploration	Charlie	2010-02-27 14:29:40

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