{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T09:58:11Z","timestamp":1772013491810,"version":"3.50.1"},"reference-count":27,"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 1 < c < (300s + 31)\/(200s + 64) be fixed. Assume that\n N ><\/jats:italic>\n 0 is a large enough number and\n \u03b5<\/jats:italic>\n > 0 is an arbitrarily small constant. This paper establish that the Diophantine inequality\n <\/jats:p>\n \n |\n p<\/jats:italic>\n 1<\/jats:sub>\n \n c<\/jats:italic>\n <\/jats:sup>\n + \u2026 +\n p<\/jats:italic>\n \n s<\/jats:italic>\n <\/jats:sub>\n \n c<\/jats:italic>\n <\/jats:sup>\n \u2212\n N<\/jats:italic>\n | <\n \u03b5<\/jats:italic>\n <\/jats:p>\n \n has a solution in prime numbers\n p<\/jats:italic>\n 1<\/jats:sub>\n ,\u2026\n \n ,p\n s<\/jats:sub>\n <\/jats:italic>\n , where\n s<\/jats:italic>\n \u2265 7 and\n s<\/jats:italic>\n is a natural number and\n p<\/jats:italic>\n 1<\/jats:sub>\n can be expressed as\n p<\/jats:italic>\n 1<\/jats:sub>\n =\n m<\/jats:italic>\n 2<\/jats:sup>\n +\n n<\/jats:italic>\n 2<\/jats:sup>\n + 1 for some integers\n m,n.<\/jats:italic>\n <\/jats:p>","DOI":"10.1051\/ita\/2026002","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T08:57:57Z","timestamp":1772009877000},"page":"4","source":"Crossref","is-referenced-by-count":0,"title":["A Diophantine inequality with one prime of the form\n p<\/i>\n =\n m<\/i>\n 2<\/sup>\n +\n n<\/i>\n 2<\/sup>\n + 1"],"prefix":"10.1051","volume":"60","author":[{"given":"Yukun","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University","place":["PR China"]}]},{"given":"Jing","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University","place":["PR China"]}]}],"member":"250","published-online":{"date-parts":[[2026,2,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.22405\/2226-8383-2023-24-4-325-334","volume":"24","author":"Goryashin","year":"2023","journal-title":"Chebyshevskii Sb."},{"key":"R2","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.jmaa.2016.03.025","volume":"440","author":"Yang","year":"2016","journal-title":"J. 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