Finite fields
Generators and irreducible polynomials over finite fields
Mathematics of Computation
Distribution of irreducible polynomials of small degrees over finite fields
Mathematics of Computation
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Explicit evaluation of certain exponential sums of binary quadratic functions
Finite Fields and Their Applications
On the number of rational points on some families of Fermat curves over finite fields
Finite Fields and Their Applications
Primitive polynomials with a prescribed coefficient
Finite Fields and Their Applications
Irreducible polynomials over finite fields with prescribed trace/prescribed constant term
Finite Fields and Their Applications
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Let @a,@b@?F"q"^"t^* and let N"t(@a,@b) denote the number of solutions (x,y)@?F"q"^"t^*xF"q"^"t^* of the equation x^q^-^1+@ay^q^-^1=@b. Recently, Moisio determined N"2(@a,@b) and evaluated N"3(@a,@b) in terms of the number of rational points on a projective cubic curve over F"q. We show that N"t(@a,@b) can be expressed in terms of the number of monic irreducible polynomials f@?F"q[x] of degree r such that f(0)=a and f(1)=b, where r|t and a,b@?F"q^* are related to @a,@b. Let I"r(a,b) denote the number of such polynomials. We prove that I"r(a,b)0 when r=3. We also show that N"3(@a,@b) can be expressed in terms of the number of monic irreducible cubic polynomials over F"q with certain prescribed trace and norm.