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
SN - 0022-314X
VL - 59
SP - 88
EP - 105
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -