(aka Brahmagupta-Fibonacci identity)

Here is the link to the Wikipedia article on this topic.

This identity “expresses the product of two sums of two squares as a sum of two squares in two different ways. Hence the set of all sums of two squares is closed under multiplication.”

So, if each of two numbers is representable as the sum of two squares, then so is their product, in two different ways, for example, (1^2 + 4^2)(2^2 + 7^2) = 26^2 + 15^2 = 30^2 + 1^2, that is,

(17 x 53) = 676 + 225 = 900 + 1 = 901

keywords:

[circular numbers]

[sum of two squares]

[Diophantine identity]

[Mathematics]

[Number Theory]

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