Thursday, May 29, 2014

Sum and squares

Given x2 - Dy2 = 1, you can get to some really cool equations using elementary methods, valid for the special cases x = 1 or -1 mod D.

Using those equations, you can get a result involving a sum, which is x+y, and squares:

x+y = n2 + (D-1)m2


2(x+y) = n2 + (D-1)m2

for some integers n and m.

I've recently explained in a post how to calculate n and m when you know x and y.

James Harris

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