Yet another Proof of an old Hat

Roland Bacher (1)

1 IF - Institut Fourier

Every odd prime number p can be written in exactly (p + 1)/2 ways as a sum ab + cd with min(a, b) > max(c, d) of two ordered products. This gives a new proof Fermat's Theorem expressing primes of the form 1 + 4N as sums of two squares 1 .

Domaines: Théorie des nombres [math.NT]

Roland Bacher. Yet another Proof of an old Hat. 2022. ⟨hal-03408135v2⟩