On strong Dickson pseudoprimes |
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| Authors: | G Kowol |
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| Affiliation: | (1) Institute for Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria |
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| Abstract: | It is known that the Lucas sequenceV
n( ,c)=an + bn,a, b being the roots ofx
2 – x + c=0 equals the Dickson polynomial
![$$g_n (\xi ,c) = \sum\limits_{i = 0}^{n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$](/content/h8532u745j778826/200_2005_Article_BF01387195_TeX2GIFIE1.gif)
.n–2i
Lidl, Müller and Oswald recently defined a number b  to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if itgn(b, c) b modn for all b. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. |
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| Keywords: | Lucas sequences Dickson polynomials Dickson pseudoprimes probabilistic prime number test |
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