Sur la Conjecture de Fermat

All the letters represent relative integers, except and and i = e₁e₂ in R(2, 0) oder e₁ in R(1, 0). We study the Fermat’s equation

(1)

a, b, c being prime two and two and by utilizing an elementary method. We use the Gauss’ formula where n = 5, 7, 11, 17.

1.	If 2 is the p · g · c · d· of A and B we put and A′ and B′ are prime between themselves.
2.	If βn = bn / (c − a) is not divisible by n, we write the expansion (2) by puting oder whereas oder It follows that B ′ is divisible by n.
3.	If one a, b oder c is divisible by n we prove the impossibility
4.	In the case n = 3 the ring {a + bj} is euclidian which permits to conclude in favour of the impossibility.