{"day":"01","doi":"10.1090/tran/8732","publication_status":"published","_id":"19490","issue":"9","scopus_import":"1","year":"2022","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2004.03331","open_access":"1"}],"status":"public","publisher":"American Mathematical Society","abstract":[{"text":"Abstract. We study integral points on the quadratic twists ED : y2 = x3 −\r\nD2x of the congruent number curve. We give upper bounds on the number of\r\nintegral points in each coset of 2ED(Q) in ED(Q) and show that their total is\r\n (3.8)rank ED(Q). We further show that the average number of non-torsion\r\nintegral points in this family is bounded above by 2. As an application we also\r\ndeduce from our upper bounds that the system of simultaneous Pell equations\r\naX2 − bY 2 = d, bY 2 − cZ2 = d for pairwise coprime positive integers a, b, c, d,\r\nhas at most  (3.6)ω(abcd) integer solutions.","lang":"eng"}],"date_created":"2025-04-05T10:50:56Z","volume":375,"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-07-10T11:51:47Z","OA_type":"green","arxiv":1,"OA_place":"repository","intvolume":"       375","page":"6675-6700","type":"journal_article","language":[{"iso":"eng"}],"date_published":"2022-09-01T00:00:00Z","citation":{"ista":"Chan S. 2022. Integral points on the congruent number curve. Transactions of the American Mathematical Society. 375(9), 6675–6700.","short":"S. Chan, Transactions of the American Mathematical Society 375 (2022) 6675–6700.","apa":"Chan, S. (2022). Integral points on the congruent number curve. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/8732\">https://doi.org/10.1090/tran/8732</a>","mla":"Chan, Stephanie. “Integral Points on the Congruent Number Curve.” <i>Transactions of the American Mathematical Society</i>, vol. 375, no. 9, American Mathematical Society, 2022, pp. 6675–700, doi:<a href=\"https://doi.org/10.1090/tran/8732\">10.1090/tran/8732</a>.","chicago":"Chan, Stephanie. “Integral Points on the Congruent Number Curve.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2022. <a href=\"https://doi.org/10.1090/tran/8732\">https://doi.org/10.1090/tran/8732</a>.","ama":"Chan S. Integral points on the congruent number curve. <i>Transactions of the American Mathematical Society</i>. 2022;375(9):6675-6700. doi:<a href=\"https://doi.org/10.1090/tran/8732\">10.1090/tran/8732</a>","ieee":"S. Chan, “Integral points on the congruent number curve,” <i>Transactions of the American Mathematical Society</i>, vol. 375, no. 9. American Mathematical Society, pp. 6675–6700, 2022."},"publication":"Transactions of the American Mathematical Society","month":"09","quality_controlled":"1","external_id":{"arxiv":["2004.03331"]},"article_type":"original","publication_identifier":{"eissn":["1088-6850"],"issn":["0002-9947"]},"author":[{"last_name":"Chan","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","full_name":"Chan, Yik Tung","first_name":"Yik Tung","orcid":"0000-0001-8467-4106"}],"oa":1,"extern":"1","title":"Integral points on the congruent number curve","oa_version":"Preprint"}