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I would like to suggest an additional meaning of ‘circular number’, namely, a number (that is, an integer) representable as the sum of two squares. That way a certain famous result glides smoothly off the tongue as, “The product of two circular numbers is itself circular.” Furthermore, I would like to suggest the term ‘semi-circular number’ for a number that is representable as the sum of two circular numbers. That way Lagrange’s four-square theorem glides smoothly off the tongue as, “Every nonnegative integer is semi-circular.”

keywords:

[two squares]

[Mathematics]

[Diophantus identity]

[Brahmagupta-Fibonacci identity]

[Number Theory]

[representation]

[ending digits]

[automorphic numbers]

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