Vasilenko, O. N. On some properties of Fermat numbers. (English. Russian original) Zbl 1061.11500 Mosc. Univ. Math. Bull. 53, No. 5, 36-38 (1998); translation from Vestn. Mosk. Univ., Ser. I 1998, No. 5, 56-58 (1998). Reviewer: V. G. Miladzhanov (Andizhan) MSC: 11A51 11Y11 PDFBibTeX XMLCite \textit{O. N. Vasilenko}, Mosc. Univ. Math. Bull. 53, No. 5, 56--58 (1998; Zbl 1061.11500); translation from Vestn. Mosk. Univ., Ser. I 1998, No. 5, 56--58 (1998)
Gundewar, G. V. Expression for factorials as the product of some power of distinct prime numbers. (English) Zbl 1050.11503 Math. Educ. 32, No. 3, 149-150 (1998). MSC: 11A51 PDFBibTeX XMLCite \textit{G. V. Gundewar}, Math. Educ. 32, No. 3, 149--150 (1998; Zbl 1050.11503)
van Albada, P. J. Factorisation of the numbers \(n^2+1\). (English) Zbl 0987.11004 Nieuw Arch. Wiskd., IV. Ser. 16, No. 3, 191-197 (1998). Reviewer: Roelof J.Stroeker (Rotterdam) MSC: 11A51 PDFBibTeX XMLCite \textit{P. J. van Albada}, Nieuw Arch. Wiskd., IV. Ser. 16, No. 3, 191--197 (1998; Zbl 0987.11004)
Gashkov, S. B. A simplified substantiation of the probabilistic Miller-Rabin primality test. (English. Russian original) Zbl 0985.11065 Discrete Math. Appl. 8, No. 6, 545-548 (1998); translation from Diskretn. Mat. 10, No. 4, 35-38 (1998). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11Y11 PDFBibTeX XMLCite \textit{S. B. Gashkov}, Discrete Math. Appl. 8, No. 6, 545--548 (1998; Zbl 0985.11065); translation from Diskretn. Mat. 10, No. 4, 35--38 (1998) Full Text: DOI
Mollin, Richard A. Fundamental number theory with applications. (English) Zbl 0943.11001 CRC Press Series on Discrete Mathematics and its Applications. Boca Raton, FL: CRC Press. xii, 439 p. (1998). Reviewer: P.Shiu (Loughborough) MSC: 11-01 11Axx 11Dxx 11Rxx 11Yxx 11A07 11A15 11A55 11Y05 11Y11 94A60 11R11 PDFBibTeX XMLCite \textit{R. A. Mollin}, Fundamental number theory with applications. Boca Raton, FL: CRC Press (1998; Zbl 0943.11001)
Brillhart, John Note on Fibonacci primality testing. (English) Zbl 0946.11003 Fibonacci Q. 36, No. 3, 222-228 (1998). Reviewer: Corey Powell (San Jose) MSC: 11A51 11B39 PDFBibTeX XMLCite \textit{J. Brillhart}, Fibonacci Q. 36, No. 3, 222--228 (1998; Zbl 0946.11003)
Pi, Xinming Searching for generalized Fermat primes. (Chinese. English summary) Zbl 1001.11056 J. Math., Wuhan Univ. 18, No. 3, 276-280 (1998). Reviewer: Wang Cun-Zheng (Chengdu) MSC: 11Y11 11A41 PDFBibTeX XMLCite \textit{X. Pi}, J. Math., Wuhan Univ. 18, No. 3, 276--280 (1998; Zbl 1001.11056)
Tsangaris, Panayiotis G. A sieve for all primes of the form \(x^2+(x+1)^2\). (English) Zbl 0968.11005 Acta Acad. Paedagog. Agriensis, Sect. Mat. (N.S.) 25, 39-53 (1998). MSC: 11A41 11A51 PDFBibTeX XMLCite \textit{P. G. Tsangaris}, Acta Acad. Paedagog. Agriensis, Sect. Mat. (N.S.) 25, 39--53 (1998; Zbl 0968.11005)
Balasubramanian, R.; Nagaraj, S. V. The least witness of a composite number. (English) Zbl 0932.11079 Okamoto, Eiji (ed.) et al., Information security. 1st international workshop, ISW ’97, Tatsunokuchi, Ishikawa, Japan, September 17–19, 1997. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1396, 66-74 (1998). Reviewer: D.R.Heath-Brown (Oxford) MSC: 11Y11 11A51 11Y16 PDFBibTeX XMLCite \textit{R. Balasubramanian} and \textit{S. V. Nagaraj}, Lect. Notes Comput. Sci. 1396, 66--74 (1998; Zbl 0932.11079)
Indlekofer, K.-H.; Jarai, A. The largest known prime pair and Germain number. (Ukrainian) Zbl 0915.11062 Sviti Mat. 4, No. 1, 9-10 (1998). Reviewer: M.P.Moklyachuk (Kyïv) MSC: 11Y11 11-04 11A41 PDFBibTeX XMLCite \textit{K. H. Indlekofer} and \textit{A. Jarai}, Sviti Mat. 4, No. 1, 9--10 (1998; Zbl 0915.11062)
Müller, Siguna A note on strong Dickson pseudoprimes. (English) Zbl 0921.11007 Appl. Algebra Eng. Commun. Comput. 9, No. 3, 247-264 (1998). Reviewer: G.Kowol (Wien) MSC: 11A51 11Y11 PDFBibTeX XMLCite \textit{S. Müller}, Appl. Algebra Eng. Commun. Comput. 9, No. 3, 247--264 (1998; Zbl 0921.11007) Full Text: DOI
Sun, Qi; Hong, Shaofang Aurifeuillian factorizations of \(q^q\pm 1\) \((q=p^n)\). (Chinese. English summary) Zbl 0915.11007 Appl. Math., Ser. A (Chin. Ed.) 13, No. 3, 342-348 (1998). Reviewer: Peter Shiu (Loughborough) MSC: 11A51 PDFBibTeX XMLCite \textit{Q. Sun} and \textit{S. Hong}, Appl. Math., Ser. A (Chin. Ed.) 13, No. 3, 342--348 (1998; Zbl 0915.11007)
Le, Maohua A note on the greatest prime factors of Fermat numbers. (English) Zbl 0937.11001 Southeast Asian Bull. Math. 22, No. 1, 41-44 (1998). Reviewer: P.Shiu (Loughborough) MSC: 11A51 11J86 PDFBibTeX XMLCite \textit{M. Le}, Southeast Asian Bull. Math. 22, No. 1, 41--44 (1998; Zbl 0937.11001)
Majumdar, A. A. K. A note on the Smarandache prime product sequence. (English) Zbl 0925.11011 Smarandache Notions J. 9, No. 1-2, 137-142 (1998). Reviewer: C.T.Le (Vail) MSC: 11A41 11A51 11B83 PDFBibTeX XMLCite \textit{A. A. K. Majumdar}, Smarandache Notions J. 9, No. 1--2, 137--142 (1998; Zbl 0925.11011)
Luca, Florian An inequality between prime powers dividing \(n!\). (English) Zbl 0925.11013 Smarandache Notions J. 9, No. 1-2, 119-123 (1998). MSC: 11A51 PDFBibTeX XMLCite \textit{F. Luca}, Smarandache Notions J. 9, No. 1--2, 119--123 (1998; Zbl 0925.11013)
Le, Maohua; Wu, Kejian A note on the primes in Samarandache unary sequence. (English) Zbl 0925.11012 Smarandache Notions J. 9, No. 1-2, 97-98 (1998). MSC: 11A51 PDFBibTeX XMLCite \textit{M. Le} and \textit{K. Wu}, Smarandache Notions J. 9, No. 1--2, 97--98 (1998; Zbl 0925.11012)
Stephan, Ralf W. Factors and primes in two Smarandache sequences. (English) Zbl 0919.11002 Smarandache Notions J. 9, No. 1-2, 4-10 (1998). Reviewer: M.Joye (Tamsui) MSC: 11-04 11A63 PDFBibTeX XMLCite \textit{R. W. Stephan}, Smarandache Notions J. 9, No. 1--2, 4--10 (1998; Zbl 0919.11002)
Grantham, Jon A probable prime test with high confidence. (English) Zbl 0930.11087 J. Number Theory 72, No. 1, 32-47 (1998). Reviewer: H.Cohn (Bowie) MSC: 11Y11 PDFBibTeX XMLCite \textit{J. Grantham}, J. Number Theory 72, No. 1, 32--47 (1998; Zbl 0930.11087) Full Text: DOI arXiv
Somer, Lawrence On Lucas \(d\)-pseudoprimes. (English) Zbl 0919.11008 Bergum, G. E. (ed.) et al., Applications of Fibonacci numbers. Volume 7: Proceedings of the 7th international research conference on Fibonacci numbers and their applications, Graz, Austria, July 15–19, 1996. Dordrecht: Kluwer Academic Publishers. 369-375 (1998). Reviewer: P.Kiss (Eger) MSC: 11A51 11B39 11Y11 PDFBibTeX XMLCite \textit{L. Somer}, in: Applications of Fibonacci numbers. Volume 7: Proceedings of the 7th international research conference on Fibonacci numbers and their applications, Graz, Austria, July 15--19, 1996. Dordrecht: Kluwer Academic Publishers. 369--375 (1998; Zbl 0919.11008)
Rotkiewicz, A. There are infinitely many arithmetical progressions formed by three different Fibonacci pseudoprimes. (English) Zbl 0926.11004 Bergum, G. E. (ed.) et al., Applications of Fibonacci numbers. Volume 7: Proceedings of the 7th international research conference on Fibonacci numbers and their applications, Graz, Austria, July 15–19, 1996. Dordrecht: Kluwer Academic Publishers. 327-332 (1998). Reviewer: P.Kiss (Eger) MSC: 11A07 11B39 11B25 11A51 PDFBibTeX XMLCite \textit{A. Rotkiewicz}, in: Applications of Fibonacci numbers. Volume 7: Proceedings of the 7th international research conference on Fibonacci numbers and their applications, Graz, Austria, July 15--19, 1996. Dordrecht: Kluwer Academic Publishers. 327--332 (1998; Zbl 0926.11004)
More, Willi Probable prime tests using Lucas sequences. (English) Zbl 1027.11505 Bergum, G. E. (ed.) et al., Applications of Fibonacci numbers. Volume 7: Proceedings of the 7th international research conference on Fibonacci numbers and their applications, Graz, Austria, July 15-19, 1996. Dordrecht: Kluwer Academic Publishers. 283-289 (1998). MSC: 11Y11 11A51 11B39 PDFBibTeX XMLCite \textit{W. More}, in: Applications of Fibonacci numbers. Volume 7: Proceedings of the 7th international research conference on Fibonacci numbers and their applications, Graz, Austria, July 15--19, 1996. Dordrecht: Kluwer Academic Publishers. 283--289 (1998; Zbl 1027.11505)
Baaz, Matthias; Zach, Richard Note on generalizing theorems in algebraically closed fields. (English) Zbl 0905.03038 Arch. Math. Logic 37, No. 5-6, 297-307 (1998). MSC: 03F07 12L99 03F20 PDFBibTeX XMLCite \textit{M. Baaz} and \textit{R. Zach}, Arch. Math. Logic 37, No. 5--6, 297--307 (1998; Zbl 0905.03038) Full Text: DOI
Atkin, A. O. L. Intelligent primality test offer. (English) Zbl 0928.11054 Buell, D. A. (ed.) et al., Computational perspectives on number theory. Proceedings of a conference in honor of A. O. L. Atkin, Chicago, IL, USA, September 1995. Providence, RI: American Mathematical Society. AMS/IP Stud. Adv. Math. 7, 1-11 (1998). Reviewer: H.Cohn (Bowie) MSC: 11Y05 11Y11 PDFBibTeX XMLCite \textit{A. O. L. Atkin}, AMS/IP Stud. Adv. Math. 7, 1--11 (1998; Zbl 0928.11054)
Young, Jeff Large primes and Fermat factors. (English) Zbl 0913.11054 Math. Comput. 67, No. 224, 1735-1738 (1998). MSC: 11Y05 11A51 11-04 11Y11 11A41 PDFBibTeX XMLCite \textit{J. Young}, Math. Comput. 67, No. 224, 1735--1738 (1998; Zbl 0913.11054) Full Text: DOI
Young, Adam; Yung, Moti Finding length-3 positive Cunningham chains and their cryptographic significance. (English) Zbl 1067.94568 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21–25, 1998. Proceedings. Berlin: Springer (ISBN 3-540-64657-4). Lect. Notes Comput. Sci. 1423, 289-298 (1998). MSC: 94A60 11Y16 PDFBibTeX XMLCite \textit{A. Young} and \textit{M. Yung}, Lect. Notes Comput. Sci. 1423, 289--298 (1998; Zbl 1067.94568) Full Text: Link
Boneh, Dan; Horwitz, Jeremy Generating a product of three primes with an unknown factorization. (English) Zbl 0916.11066 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21–25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 237-251 (1998). Reviewer: Ian F.Blake (Palo Alto) MSC: 11Y05 94A60 11T71 PDFBibTeX XMLCite \textit{D. Boneh} and \textit{J. Horwitz}, Lect. Notes Comput. Sci. 1423, 237--251 (1998; Zbl 0916.11066)
Deshouillers, J.-M.; te Riele, H. J. J.; Saouter, Y. New experimental results concerning the Goldbach conjecture. (English) Zbl 0957.11044 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21-25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 204-215 (1998). MSC: 11P32 11Y99 PDFBibTeX XMLCite \textit{J. M. Deshouillers} et al., Lect. Notes Comput. Sci. 1423, 204--215 (1998; Zbl 0957.11044)
Morain, F. Primality proving using elliptic curves: An update. (English) Zbl 0908.11061 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21–25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 111-127 (1998). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11Y11 11G05 14H52 11A51 PDFBibTeX XMLCite \textit{F. Morain}, Lect. Notes Comput. Sci. 1423, 111--127 (1998; Zbl 0908.11061)
Mihăilescu, Preda Cyclotomy primality proving – recent developments. (English) Zbl 0908.11060 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21–25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 95-110 (1998). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11Y11 11R18 11A51 PDFBibTeX XMLCite \textit{P. Mihăilescu}, Lect. Notes Comput. Sci. 1423, 95--110 (1998; Zbl 0908.11060)
Rotkiewicz, A. Arithmetical progressions formed by Lucas pseudoprimes. (English) Zbl 0917.11010 Győry, Kálmán (ed.) et al., Number theory. Diophantine, computational and algebraic aspects. Proceedings of the international conference, Eger, Hungary, July 29–August 2, 1996. Berlin: de Gruyter. 465-472 (1998). Reviewer: Štefan Porubský (Praha) MSC: 11B39 11B25 11A51 11Y11 PDFBibTeX XMLCite \textit{A. Rotkiewicz}, in: Number theory. Diophantine, computational and algebraic aspects. Proceedings of the international conference, Eger, Hungary, July 29--August 2, 1996. Berlin: de Gruyter. 465--472 (1998; Zbl 0917.11010)
Schwarz, Friedrich Introduction to elementary number theory. Interactive book with MuPAD CD. (Einführung in die elementare Zahlentheorie. Interaktives Buch mit MuPAD CD.) (German) Zbl 1005.11001 MuPAD Lectures. Stuttgart: B. G. Teubner. 220 S. (1998). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11-01 11-04 11Yxx 11Y05 11Axx 11A55 11Y11 11D09 PDFBibTeX XMLCite \textit{F. Schwarz}, Einführung in die elementare Zahlentheorie. Interaktives Buch mit MuPAD CD. Stuttgart: B. G. Teubner (1998; Zbl 1005.11001)
Welschenbach, Michael Cryptography in C and C++. Number theoretic foundations, computer arithmetic with large numbers, cryptographic tools. (Kryptographie in C und C++. Zahlentheoretische Grundlagen, Computer-Arithmetik mit großen Zahlen, kryptographische Tools.) (English) Zbl 0917.94011 Berlin: Springer. xii, 327 p. (1998). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 94A60 11T71 94-01 11-01 11-04 11Y99 PDFBibTeX XMLCite \textit{M. Welschenbach}, Kryptographie in C und C++. Zahlentheoretische Grundlagen, Computer-Arithmetik mit großen Zahlen, kryptographische Tools. Berlin: Springer (1998; Zbl 0917.94011)
Kumanduri, R.; Romero, Cristina Number theory with computer applications. (English) Zbl 0902.11001 Upper Saddle River, NJ: Prentice Hall. xiii, 543 p. (1998). Reviewer: P.Shiu (Loughborough) MSC: 11-01 11Y05 11Y11 94A60 11A07 11A15 11A51 11A55 PDFBibTeX XMLCite \textit{R. Kumanduri} and \textit{C. Romero}, Number theory with computer applications. Upper Saddle River, NJ: Prentice Hall (1998; Zbl 0902.11001)
Müller, Siguna M. S. On strong Lucas pseudoprimes. (English) Zbl 0922.11006 Contributions to general algebra 10. Selection of lectures given at the conference on general algebra, Klagenfurt, Austria, May 29–June 1, 1997. Klagenfurt: Verlag Johannes Heyn. 237-249 (1998). Reviewer: J.Sorenson (Indianapolis) MSC: 11A51 11Y11 11B39 PDFBibTeX XMLCite \textit{S. M. S. Müller}, Contrib. Gen. Algebra 10, 237--249 (1998; Zbl 0922.11006)
Saouter, Yannick Checking the odd Goldbach conjecture up to \(10^{20}\). (English) Zbl 0913.11044 Math. Comput. 67, No. 222, 863-866 (1998). Reviewer: A.Zaccagnini (Parma) MSC: 11P32 11Y11 PDFBibTeX XMLCite \textit{Y. Saouter}, Math. Comput. 67, No. 222, 863--866 (1998; Zbl 0913.11044) Full Text: DOI
Williams, Hugh C. Édouard Lucas and primality testing. (English) Zbl 1155.11363 Canadian Mathematical Society Series of Monographs and Advanced Texts 22. New York, NY: John Wiley & Sons (ISBN 0-471-14852-0/hbk). xviii, 525 p. (1998). Reviewer: Olaf Ninnemann (Berlin) MSC: 11Y11 11-03 11-01 11Y05 68-03 11A51 01A60 01A70 PDFBibTeX XMLCite \textit{H. C. Williams}, Édouard Lucas and primality testing. New York, NY: John Wiley \& Sons (1998; Zbl 1155.11363)
Björn, Anders; Riesel, Hans Factors of generalized Fermat numbers. (English) Zbl 0890.11002 Math. Comput. 67, No. 221, 441-446 (1998); table errata ibid. 74, No. 252, 2099 (2005). MSC: 11-04 11A51 11Y05 11Y11 PDFBibTeX XMLCite \textit{A. Björn} and \textit{H. Riesel}, Math. Comput. 67, No. 221, 441--446 (1998; Zbl 0890.11002) Full Text: DOI
Pinch, Richard G. E. The Carmichael numbers up to \(10^{16}\). arXiv:math/9803082 Preprint, arXiv:math/9803082 [math.NT] (1998). MSC: 11Y11 11A51 11Y70 BibTeX Cite \textit{R. G. E. Pinch}, ``The Carmichael numbers up to $10^{16}$'', Preprint, arXiv:math/9803082 [math.NT] (1998) Full Text: arXiv
Pinch, Richard G. E. Economical numbers. arXiv:math/9802046 Preprint, arXiv:math/9802046 [math.NT] (1998). MSC: 11A63 11A25 11A51 BibTeX Cite \textit{R. G. E. Pinch}, ``Economical numbers'', Preprint, arXiv:math/9802046 [math.NT] (1998) Full Text: arXiv