Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF (q) and conversely. This leads to an algebraic proof ofâ€¦ (More)

The study of finite projective planes involves planar functions, namely, functions f : Fq â†’ Fq such that, for each a âˆˆ F âˆ— q , the function c 7â†’ f(c + a) âˆ’ f(c) is a bijection on Fq. Planar functionsâ€¦ (More)

We derive the factorizations of the Dickson polynomials Dn(X, a) and En(X, a), and of the bivariate Dickson polynomials Dn(X, a) âˆ’ Dn(Y, a), over any finite field. Our proofs are significantlyâ€¦ (More)

We present a family of indecomposable polynomials of non prime-power degree over the finite field of three elements which are permutation polynomials over infinitely many finite extensions of theâ€¦ (More)

The Mordellâ€“Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection ofâ€¦ (More)

Several authors have considered take-away games where the players alternately remove a positive number of counters from a single pile, the player removing the last counter being the winner. On hisâ€¦ (More)

For f(X) âˆˆ Z[X], let Df (n) be the least positive integer k for which f(1), . . . , f(n) are distinct modulo k. Several results have been proven about the function Df in recent years, culminating inâ€¦ (More)

We present a method for factoring polynomials of the shape f(X)âˆ’ f(Y ), where f is a univariate polynomial over a field k. We then apply this method in the case when f is a member of the infiniteâ€¦ (More)

We construct a tower of function fields F0 âŠ‚ F1 âŠ‚ . . . over a finite field such that every place of every Fi ramifies in the tower and lim genus(Fi)/[Fi : F0] <âˆž. We also construct a tower in whichâ€¦ (More)