{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T08:54:06Z","timestamp":1774947246118,"version":"3.50.1"},"reference-count":14,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T00:00:00Z","timestamp":1774915200000},"content-version":"vor","delay-in-days":89,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12361002"],"award-info":[{"award-number":["12361002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004479","name":"Natural Science Foundation of Jiangxi Province","doi-asserted-by":"publisher","award":["20224BAB201001"],"award-info":[{"award-number":["20224BAB201001"]}],"id":[{"id":"10.13039\/501100004479","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the conference"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"accepted":{"date-parts":[[2026,2,26]]},"published-print":{"date-parts":[[2026]]},"abstract":"\n Let \u03bb\n 1<\/jats:sub>\n , \u03bb\n 2<\/jats:sub>\n , \u03bb\n 3<\/jats:sub>\n , \u03bb\n 4<\/jats:sub>\n , \u03bb\n 5<\/jats:sub>\n be nonzero real numbers, neither all positive nor all negative and \u03bb\n 1<\/jats:sub>\n \/\u03bb\n 2<\/jats:sub>\n be an irrational number. Let\n V<\/jats:italic>\n be a well-spaced sequence and\n \u03b4<\/jats:italic>\n > 0. For arbitrary \u025b > 0, we show that the quantity of\n v<\/jats:bold>\n \u2208\n V<\/jats:italic>\n with\n v<\/jats:italic>\n \u2264\n N<\/jats:italic>\n making the inequality\n <\/jats:p>\n \n |\u03bb\n 1<\/jats:sub>\n p<\/jats:italic>\n 1<\/jats:sub>\n 2<\/jats:sup>\n + \u03bb\n 2<\/jats:sub>\n p<\/jats:italic>\n 2<\/jats:sub>\n 2<\/jats:sup>\n + \u03bb\n 3<\/jats:sub>\n p<\/jats:italic>\n 3<\/jats:sub>\n 4<\/jats:sup>\n + \u03bb\n 4<\/jats:sub>\n p<\/jats:italic>\n 4<\/jats:sub>\n 4<\/jats:sup>\n + \u03bb\n 5<\/jats:sub>\n p<\/jats:italic>\n 5<\/jats:sub>\n 4<\/jats:sup>\n \u2212 v| < v\n \u2212\u03b4<\/jats:sup>\n <\/jats:p>\n \n unsolvable in primes\n p<\/jats:italic>\n 1<\/jats:sub>\n ,\n p<\/jats:italic>\n 2<\/jats:sub>\n ,\n p<\/jats:italic>\n 3<\/jats:sub>\n ,\n p<\/jats:italic>\n 4<\/jats:sub>\n ,\n p<\/jats:italic>\n 5<\/jats:sub>\n does not exceed\n O<\/jats:italic>\n (\n N<\/jats:italic>\n \n 6\/7 + 2\n \u03b4<\/jats:italic>\n +\n \u03b5<\/jats:italic>\n <\/jats:sup>\n ).\n <\/jats:p>","DOI":"10.1051\/ita\/2026013","type":"journal-article","created":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T07:51:36Z","timestamp":1774943496000},"page":"12","source":"Crossref","is-referenced-by-count":0,"title":["Diophantine approximation with two squares and three biquadrates of primes"],"prefix":"10.1051","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9872-7399","authenticated-orcid":false,"given":"Yu","family":"Fu","sequence":"first","affiliation":[{"name":"Nanchang, Jiangxi 330031, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liqun","family":"Hu","sequence":"additional","affiliation":[{"name":"Nanchang, Jiangxi 330031, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6468-0900","authenticated-orcid":false,"given":"Siqi","family":"Liu","sequence":"additional","affiliation":[{"name":"Nanchang, Jiangxi 330031, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Yang","sequence":"additional","affiliation":[{"name":"Nanchang, Jiangxi 330031, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2026,3,31]]},"reference":[{"key":"R1","unstructured":"Hooley C., On a new approach to various problems of Waring's type, in Recent Progress in Analytic Number Theory, Vol. 1. Academic Press, Durham, London (2023) 127\u2013191."},{"key":"R2","first-page":"153","volume":"60","author":"Friedlander","year":"2014","journal-title":"Mathematics"},{"key":"R3","doi-asserted-by":"crossref","first-page":"369","DOI":"10.4064\/aa162-4-4","volume":"162","author":"Zhao","year":"2014","journal-title":"Acta Arith."},{"key":"R4","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1216\/rmj.2020.50.355","volume":"50","author":"Zhu","year":"2020","journal-title":"Rocky Mountain J. Math."},{"key":"R5","first-page":"18","volume":"54","author":"Liu","year":"2025","journal-title":"Adv. Math, Chin. Ser."},{"key":"R6","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1112\/jlms\/s1-21.3.185","volume":"21","author":"Davenport","year":"1946","journal-title":"J. Lond. Math. Soc."},{"key":"R7","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1007\/s11139-019-00167-8","volume":"52","author":"Qu","year":"2020","journal-title":"Ramanujan J."},{"key":"R8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0305004105008819","volume":"140","author":"Harman","year":"2006","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"R9","first-page":"83","volume":"51","author":"Harman","year":"2005","journal-title":"Mathematics"},{"key":"R10","unstructured":"Titchmarsh E.C., The Theory of the Riemann Zeta-Function, 2nd edn. Oxford University Press, Oxford (1986)."},{"key":"R11","first-page":"249","volume":"28","author":"Harman","year":"1981","journal-title":"Mathematics"},{"key":"R12","doi-asserted-by":"crossref","first-page":"149","DOI":"10.21136\/CMJ.2018.0388-16","volume":"68","author":"Ge","year":"2018","journal-title":"Czech. Math. J."},{"key":"R13","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s11139-022-00587-z","volume":"60","author":"Li","year":"2023","journal-title":"Ramanujan J."},{"key":"R14","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.jnt.2017.04.013","volume":"180","author":"Wang","year":"2017","journal-title":"J. Number Theory."}],"container-title":["RAIRO - Theoretical Informatics and Applications"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ita.org\/10.1051\/ita\/2026013\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T07:51:40Z","timestamp":1774943500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ita.org\/10.1051\/ita\/2026013"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":14,"alternative-id":["ita20260007"],"URL":"https:\/\/doi.org\/10.1051\/ita\/2026013","relation":{},"ISSN":["0988-3754","2804-7346"],"issn-type":[{"value":"0988-3754","type":"print"},{"value":"2804-7346","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]}}}