THEOREM OF THE DAY: Fermat’s Two-Squares Theorem

Theorem

An odd prime number p may be expressed as a sum of two squares if and only if

$p ≡ 1 (mod 4)$.

Click on the image.

This theorem was discovered by Fermat in 1640 and by Albert Girard in 1632, the year of his death. The first published proof is due to Euler in 1754; that given here is an example of Hermann Minkowski’s ‘Geometry of Numbers’, developed in the 1890s