sums of two squares
This was presented by Leonardo Fibonacci in 1225 (in Liber quadratorum), but was known also by Brahmagupta and already by Diophantus of Alexandria (III book of his Arithmetica).
The proof of the equation may utilize Gaussian integers as follows:
Note 1. The equation (1) is the special case
of Lagrange’s identity.
Note 2. Similarly as (1), one can derive the identity
Thus in most cases, we can get two different nontrivial sum forms (i.e. without a zero addend) for a given product of two sums of squares. For example, the product
attains the two forms and .
|Title||sums of two squares|
|Date of creation||2013-11-19 16:28:21|
|Last modified on||2013-11-19 16:28:21|
|Last modified by||pahio (2872)|