On strong Dickson pseudoprimes
Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lid...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kowol, G. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1992 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 1992 |
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| Übergeordnetes Werk: |
Enthalten in: Applicable algebra in engineering, communication and computing - Springer-Verlag, 1990, 3(1992), 2 vom: Juni, Seite 129-138 |
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| Übergeordnetes Werk: |
volume:3 ; year:1992 ; number:2 ; month:06 ; pages:129-138 |
| Links: |
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| DOI / URN: |
10.1007/BF01387195 |
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OLC2075493677 |
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| 245 | 1 | 0 | |a On strong Dickson pseudoprimes |
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| 520 | |a Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. | ||
| 650 | 4 | |a Lucas sequences | |
| 650 | 4 | |a Dickson polynomials | |
| 650 | 4 | |a Dickson pseudoprimes | |
| 650 | 4 | |a probabilistic prime number test | |
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10.1007/BF01387195 doi (DE-627)OLC2075493677 (DE-He213)BF01387195-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Kowol, G. verfasserin aut On strong Dickson pseudoprimes 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1992 Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. Lucas sequences Dickson polynomials Dickson pseudoprimes probabilistic prime number test Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 3(1992), 2 vom: Juni, Seite 129-138 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:3 year:1992 number:2 month:06 pages:129-138 https://doi.org/10.1007/BF01387195 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 AR 3 1992 2 06 129-138 |
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10.1007/BF01387195 doi (DE-627)OLC2075493677 (DE-He213)BF01387195-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Kowol, G. verfasserin aut On strong Dickson pseudoprimes 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1992 Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. Lucas sequences Dickson polynomials Dickson pseudoprimes probabilistic prime number test Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 3(1992), 2 vom: Juni, Seite 129-138 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:3 year:1992 number:2 month:06 pages:129-138 https://doi.org/10.1007/BF01387195 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 AR 3 1992 2 06 129-138 |
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10.1007/BF01387195 doi (DE-627)OLC2075493677 (DE-He213)BF01387195-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Kowol, G. verfasserin aut On strong Dickson pseudoprimes 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1992 Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. Lucas sequences Dickson polynomials Dickson pseudoprimes probabilistic prime number test Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 3(1992), 2 vom: Juni, Seite 129-138 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:3 year:1992 number:2 month:06 pages:129-138 https://doi.org/10.1007/BF01387195 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 AR 3 1992 2 06 129-138 |
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10.1007/BF01387195 doi (DE-627)OLC2075493677 (DE-He213)BF01387195-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Kowol, G. verfasserin aut On strong Dickson pseudoprimes 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1992 Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. Lucas sequences Dickson polynomials Dickson pseudoprimes probabilistic prime number test Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 3(1992), 2 vom: Juni, Seite 129-138 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:3 year:1992 number:2 month:06 pages:129-138 https://doi.org/10.1007/BF01387195 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 AR 3 1992 2 06 129-138 |
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10.1007/BF01387195 doi (DE-627)OLC2075493677 (DE-He213)BF01387195-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Kowol, G. verfasserin aut On strong Dickson pseudoprimes 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1992 Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. Lucas sequences Dickson polynomials Dickson pseudoprimes probabilistic prime number test Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 3(1992), 2 vom: Juni, Seite 129-138 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:3 year:1992 number:2 month:06 pages:129-138 https://doi.org/10.1007/BF01387195 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 AR 3 1992 2 06 129-138 |
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English |
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Enthalten in Applicable algebra in engineering, communication and computing 3(1992), 2 vom: Juni, Seite 129-138 volume:3 year:1992 number:2 month:06 pages:129-138 |
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Enthalten in Applicable algebra in engineering, communication and computing 3(1992), 2 vom: Juni, Seite 129-138 volume:3 year:1992 number:2 month:06 pages:129-138 |
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on strong dickson pseudoprimes |
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On strong Dickson pseudoprimes |
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Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. © Springer-Verlag 1992 |
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Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined. © Springer-Verlag 1992 |
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Abstract It is known that the Lucas sequenceVn(ξ,c)=$ a^{n} $ + $ b^{n} $,a, b being the roots ofx2 − ξx + c=0 equals the Dickson polynomial$$g_n (\xi ,c) = \sum\limits_{i = 0}^{[n/2]} {\frac{n}{{n - 1}}} \left( {\begin{array}{*{20}c} {n - 1} \\ i \\ \end{array} } \right)( - c)^i $$.$ ξ^{n−2i} $ Lidl, Müller and Oswald recently defined a number bεℤ to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [$ itg_{n} $(b, c)≡b modn for all bεℤ. 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. © Springer-Verlag 1992 |
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