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maxal · 2009-09-17, 15:32

Quote:

Originally Posted by maxal

$(m+qi)^2 - 4n = \left( \frac{n}{d_i} - d_i \right)^2$ 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.