Solving $X^{q+1}+X+a=0$ over Finite Fields

Kwang Ho Kim, Junyop Choe, Sihem Mesnager

Solving the equation $P_a(X):=X^{q+1}+X+a=0$ over finite field $\GF{Q}$, where $Q=p^n,q=p^k$ and $p$ is a prime, arises in many different contexts including finite geometry, the i…