Dickson polynomial discriminators

Pieter Moree; Gary L. Mullen

doi:10.1006/jnth.1996.0089

Dickson polynomial discriminators

Pieter Moree
, Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

For an integer a the integral Dickson polynomial of degree j ≥ 1 is defined by g_j(X, a) = ∑ ^[j/2] _{i = 0} j/j - i (j - i i) (-a)ⁱ X^{j - 2i}. We consider the Dickson discriminator problem, that is we study the problem of finding for all integers a and all natural numbers j and n, the smallest positive integer k for which the integers g_j(1, a), g_j(2, a), ..., g_j(n, a) are distinct modulo k.

Original language	English (US)
Pages (from-to)	88-105
Number of pages	18
Journal	Journal of Number Theory
Volume	59
Issue number	1
DOIs	https://doi.org/10.1006/jnth.1996.0089
State	Published - Jul 1996

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1006/jnth.1996.0089

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@article{94bfc6600ee045cbb73e6144d5dba01a,

title = "Dickson polynomial discriminators",

abstract = "For an integer a the integral Dickson polynomial of degree j ≥ 1 is defined by gj(X, a) = ∑ [j/2] i = 0 j/j - i (j - i i) (-a)i Xj - 2i. We consider the Dickson discriminator problem, that is we study the problem of finding for all integers a and all natural numbers j and n, the smallest positive integer k for which the integers gj(1, a), gj(2, a), ..., gj(n, a) are distinct modulo k.",

author = "Pieter Moree and Mullen, \{Gary L.\}",

note = "Funding Information: * Supported by the Netherlands Organization for Scientific Research (NWO). E-mail: moree mpim-bonn.mpg.de. -This author would like to thank the National Security Agency for partial support under Grant MDA904-92-H-3044. E-mail: mullen math.psu.edu.",

year = "1996",

month = jul,

doi = "10.1006/jnth.1996.0089",

language = "English (US)",

volume = "59",

pages = "88--105",

journal = "Journal of Number Theory",

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AU - Moree, Pieter

AU - Mullen, Gary L.

N1 - Funding Information: * Supported by the Netherlands Organization for Scientific Research (NWO). E-mail: moree mpim-bonn.mpg.de. -This author would like to thank the National Security Agency for partial support under Grant MDA904-92-H-3044. E-mail: mullen math.psu.edu.

PY - 1996/7

Y1 - 1996/7

N2 - For an integer a the integral Dickson polynomial of degree j ≥ 1 is defined by gj(X, a) = ∑ [j/2] i = 0 j/j - i (j - i i) (-a)i Xj - 2i. We consider the Dickson discriminator problem, that is we study the problem of finding for all integers a and all natural numbers j and n, the smallest positive integer k for which the integers gj(1, a), gj(2, a), ..., gj(n, a) are distinct modulo k.

AB - For an integer a the integral Dickson polynomial of degree j ≥ 1 is defined by gj(X, a) = ∑ [j/2] i = 0 j/j - i (j - i i) (-a)i Xj - 2i. We consider the Dickson discriminator problem, that is we study the problem of finding for all integers a and all natural numbers j and n, the smallest positive integer k for which the integers gj(1, a), gj(2, a), ..., gj(n, a) are distinct modulo k.

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U2 - 10.1006/jnth.1996.0089

DO - 10.1006/jnth.1996.0089

M3 - Article

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SN - 0022-314X

VL - 59

SP - 88

EP - 105

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

Dickson polynomial discriminators

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