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Old 2009-09-17, 15:32   #9
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Feb 2005

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Originally Posted by maxal View Post
(m+qi)^2 - 4n = \left( \frac{n}{d_i} - d_i \right)^2 for i=1,2,\dots,k
form a sequence of k squares whose second differences equal the constant 2 q^2.
I forgot to mention an important property - this sequence does not represent squares of consecutive terms of an arithmetic progression.

While the sequence
(m+qi)^2 = \left( \frac{n}{d_i} + d_i \right)^2
also has the second differences equal 2 q^2, it is a trivial and uninteresting sequence of this kind.

Last fiddled with by maxal on 2009-09-17 at 15:35
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