{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T04:25:18Z","timestamp":1777091118884,"version":"3.51.4"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"218","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We give bounds on the number of pairs\n \n \n \n \n (<\/mml:mo>\n P<\/mml:mi>\n ,<\/mml:mo>\n Q<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n (P,Q)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n with\n \n \n \n \n 0<\/mml:mn>\n \n \u2264\n \n <\/mml:mo>\n P<\/mml:mi>\n ,<\/mml:mo>\n Q<\/mml:mi>\n ><\/mml:mo>\n n<\/mml:mi>\n <\/mml:mrow>\n 0\\le P,Q>n<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n such that a composite number\n \n \n \n n<\/mml:mi>\n n<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n is a strong Lucas pseudoprime with respect to the parameters\n \n \n \n \n (<\/mml:mo>\n P<\/mml:mi>\n ,<\/mml:mo>\n Q<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n (P,Q)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>","DOI":"10.1090\/s0025-5718-97-00836-3","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"869-881","source":"Crossref","is-referenced-by-count":8,"title":["The Rabin-Monier theorem for Lucas pseudoprimes"],"prefix":"10.1090","volume":"66","author":[{"given":"F.","family":"Arnault","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1997]]},"reference":[{"issue":"209","key":"1","doi-asserted-by":"publisher","first-page":"355","DOI":"10.2307\/2153340","article-title":"Rabin-Miller primality test: composite numbers which pass it","volume":"64","author":"Arnault, F.","year":"1995","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"2","doi-asserted-by":"crossref","unstructured":"\\bysame, Constructing Carmichael numbers which are strong pseudoprimes to several bases, J. Symbolic Comput. 20 (1995), 151\u2013161.","DOI":"10.1006\/jsco.1995.1042"},{"key":"3","unstructured":"F. Arnault and G. Robin, Sur une fonction associ\u00e9e aux entiers quadratiques, Preprint."},{"issue":"152","key":"4","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.2307\/2006406","article-title":"Lucas pseudoprimes","volume":"35","author":"Baillie, Robert","year":"1980","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"204","key":"5","doi-asserted-by":"publisher","first-page":"915","DOI":"10.2307\/2153262","article-title":"On strong pseudoprimes to several bases","volume":"61","author":"Jaeschke, Gerhard","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"6","unstructured":"Z. Mo and J. P. Jones, A new probabilistic primality test using Lucas sequences, Preprint."},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0304-3975(80)90007-9","article-title":"Evaluation and comparison of two efficient probabilistic primality testing algorithms","volume":"12","author":"Monier, Louis","year":"1980","journal-title":"Theoret. Comput. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0304-3975","issn-type":"print"},{"issue":"151","key":"8","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.2307\/2006210","article-title":"The pseudoprimes to 25\u22c510\u2079","volume":"35","author":"Pomerance, Carl","year":"1980","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"9","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/0022-314X(80)90084-0","article-title":"Probabilistic algorithm for testing primality","volume":"12","author":"Rabin, Michael O.","year":"1980","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"1","key":"10","doi-asserted-by":"publisher","first-page":"133","DOI":"10.4153\/CMB-1977-025-9","article-title":"On numbers analogous to the Carmichael numbers","volume":"20","author":"Williams, H. C.","year":"1977","journal-title":"Canad. Math. Bull.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-4395","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00836-3\/S0025-5718-97-00836-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00836-3\/S0025-5718-97-00836-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:27:42Z","timestamp":1776720462000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00836-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"references-count":10,"journal-issue":{"issue":"218","published-print":{"date-parts":[[1997,4]]}},"alternative-id":["S0025-5718-97-00836-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-97-00836-3","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1997]]}}}