On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2
Résumé
Let t be an integer ≥ 3 such that t ≡ 1 mod 4. The absolute irreducibility of the polynomial ϕt(x,y)=xt+yt+1+(x+y+1)t(x+y)(x+1)(y+1) (over F2) plays an important role in the study of APN functions. We prove that this polynomial is absolutely irreducible under the assumptions that the largest odd integer which divides t − 1 is large enough and can not be written in a specific form.