{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T01:25:08Z","timestamp":1660267508343},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5763,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1998,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In [4] it is shown that only using exponentiation can one prove the existence of non trivial solutions of Pell equations in <jats:italic>I<\/jats:italic>\u0394<jats:sub>0<\/jats:sub>. However, in this paper we will prove that any Pell equation has a non trivial solution modulo <jats:italic>m<\/jats:italic> for every <jats:italic>m<\/jats:italic> in <jats:italic>I<\/jats:italic>\u0394<jats:sub>0<\/jats:sub>.<\/jats:p>","DOI":"10.2307\/2586838","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:17Z","timestamp":1146938477000},"page":"402-410","source":"Crossref","is-referenced-by-count":2,"title":["Solving Pell equations locally in models of <i>I<\/i>\u0394<sub>0<\/sub>"],"prefix":"10.1017","volume":"63","author":[{"given":"Paola","family":"D'Aquino","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200014961_ref007","volume-title":"Algebra","author":"Lang","year":"1993"},{"key":"S0022481200014961_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90076-E"},{"key":"S0022481200014961_ref001","unstructured":"Bennett, J. H. , On spectra, Doctoral dissertation , Princeton University, 1962."},{"key":"S0022481200014961_ref010","first-page":"667","article-title":"A definition of exponentiation by a bounded arithmetical formula","volume":"24","author":"Pudl\u00e0k","year":"1983","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0022481200014961_ref005","unstructured":"Dimitracopoulos, C. , Matijasevic theorem and fragments of arithmetic, Ph.D. thesis , Manchester, 1980."},{"key":"S0022481200014961_ref004","volume-title":"Annals of Pure and Applied Logic","author":"D'Aquino","year":"1996"},{"key":"S0022481200014961_ref008","first-page":"494","volume":"36","author":"Parikh","year":"1971","journal-title":"Existence andfeasibility in arithmetic"},{"key":"S0022481200014961_ref003","first-page":"12","volume":"57","author":"D'Aquino","year":"1992","journal-title":"Local behaviour of Chebyshev theorem in models of I\u03940"},{"key":"S0022481200014961_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90096-5"},{"key":"S0022481200014961_ref009","first-page":"1235","volume":"53","author":"Paris","year":"1988","journal-title":"Provability of the pigeonhole principle and the existence of infinitely many primes"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200014961","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T12:14:33Z","timestamp":1628597673000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200014961\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1998,6]]}},"alternative-id":["S0022481200014961"],"URL":"https:\/\/doi.org\/10.2307\/2586838","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,6]]}}}