Thread: Diophantine Question View Single Post
2009-09-17, 15:32   #9
maxal

Feb 2005

22×32×7 Posts

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.

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