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On the number of directions determined by a pair of functions over a prime field |
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| Authors: | Simeon Ball |
| Affiliation: | a Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Mòdul C3, Campus Nord, 08034 Barcelona, Spain b Eötvös University Budapest, Pázmány P. sétány 1/c, Budapest, Hungary H-1117 |
| Abstract: | A three-dimensional analogue of the classical direction problem is proposed and an asymptotically sharp bound for the number of directions determined by a non-planar set in AG(3,p), p prime, is proved. Using the terminology of permutation polynomials the main result states that if there are more than  pairs  with the property that f(x)+ag(x)+bx is a permutation polynomial, then there exist elements c,d,e∈Fp with the property that f(x)=cg(x)+dx+e. |
| Keywords: | Permutation polynomials Directions determined by a function Functions over a finite field |
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