A complete classification of permutation binomials of the form $X^r(X^{q-1}+a)$ over finite fields

Xiang Fan

We classify, for every prime power $q$ and every $e⩾2$, the permutation binomials $X^r(X^{q-1}+a)$ over ${\mathbb{F}}_{q^e}$. Writing ${\ell }_j(q)=(q^j-1)/(q-1)$, such a binomia…