Abstract
The following theorems are famous landmarks in the history of number theory.Theorem 1 (Fermat-Euler): A number is representable as a sum of two squares if, and only if, it has the form PQ2, where P is free of prime divisors q ≡ 3 (mod 4).Theorem 2 (Lagrange): Every number is representable as a sum of four squares.Theorem 3 (Gauss-Legendre): A number is representable as a sum of three squares if, and only if, it is not of the form 4a (8n + 7).
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