TY - JOUR

T1 - Dickson polynomial discriminators

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

AN - SCOPUS:0030187023

VL - 59

SP - 88

EP - 105

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -