{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T09:58:10Z","timestamp":1772013490391,"version":"3.50.1"},"reference-count":21,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T00:00:00Z","timestamp":1771977600000},"content-version":"vor","delay-in-days":55,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171286"],"award-info":[{"award-number":["12171286"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"accepted":{"date-parts":[[2025,12,31]]},"published-print":{"date-parts":[[2026]]},"abstract":"\n Let\n k<\/jats:italic>\n \u2265 7 be fixed, and\n v<\/jats:italic>\n = (55\n k<\/jats:italic>\n + 556)\/(26\n k<\/jats:italic>\n + 672),1 <\n d<\/jats:italic>\n <\n c<\/jats:italic>\n <\n v<\/jats:italic>\n , 1 <\n \u03bc<\/jats:italic>\n <\n \u03bd<\/jats:italic>\n <\n k<\/jats:italic>\n 1\u2212<\/jats:sup>\n \n d\/c<\/jats:sup>\n <\/jats:italic>\n and\n \u03bc<\/jats:italic>\n \u2264\n N<\/jats:italic>\n 2<\/jats:sub>\n \/\n N<\/jats:italic>\n 1<\/jats:sub>\n d\/c<\/jats:sup>\n \u2264\n v<\/jats:italic>\n . Suppose that\n N<\/jats:italic>\n \u2032<\/jats:sup>\n 1<\/jats:sub>\n ,\n N<\/jats:italic>\n \u2032<\/jats:sup>\n 2<\/jats:sub>\n > 0 are real numbers, and that\n N<\/jats:italic>\n 1<\/jats:sub>\n ,\n N<\/jats:italic>\n 2<\/jats:sub>\n are real numbers satisfying\n N<\/jats:italic>\n 1<\/jats:sub>\n >\n N<\/jats:italic>\n \u2032<\/jats:sup>\n 1<\/jats:sub>\n and\n N<\/jats:italic>\n 2<\/jats:sub>\n >\n N<\/jats:italic>\n \u2032<\/jats:sup>\n 2<\/jats:sub>\n . Then we prove the system of two Diophantine inequalities\n <\/jats:p>\n \n |\n p<\/jats:italic>\n 1<\/jats:sub>\n c<\/jats:sup>\n + \u2026 +\n p<\/jats:italic>\n k<\/jats:sub>\n c<\/jats:sup>\n \u2212\n N<\/jats:italic>\n 1<\/jats:sub>\n | <\n N<\/jats:italic>\n 1<\/jats:sub>\n \u2212(1\/c)(v\u2212c)<\/jats:sup>\n log\n 195<\/jats:sup>\n N<\/jats:italic>\n 1<\/jats:sub>\n ,\n <\/jats:p>\n \n |\n p<\/jats:italic>\n 1<\/jats:sub>\n d<\/jats:sup>\n + \u2026 +\n p<\/jats:italic>\n k<\/jats:sub>\n d<\/jats:sup>\n \u2212\n N<\/jats:italic>\n 2<\/jats:sub>\n | <\n N<\/jats:italic>\n 2<\/jats:sub>\n \u2212(1\/d)(v\u2212d)<\/jats:sup>\n log\n 195<\/jats:sup>\n N<\/jats:italic>\n 2<\/jats:sub>\n <\/jats:p>\n \n has prime solutions\n p<\/jats:italic>\n 1<\/jats:sub>\n ,\u2026,\n \n p\n k<\/jats:sub>\n <\/jats:italic>\n .\n <\/jats:p>","DOI":"10.1051\/ita\/2026003","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T08:57:57Z","timestamp":1772009877000},"page":"3","source":"Crossref","is-referenced-by-count":0,"title":["A system of two Diophantine inequalities with primes"],"prefix":"10.1051","volume":"60","author":[{"given":"Yanjun","family":"Dong","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University","place":["PR China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University","place":["PR China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2026,2,25]]},"reference":[{"key":"R1","first-page":"105","volume":"30","author":"Piatetski-Shapiro","year":"1952","journal-title":"Math. 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