{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:01:13Z","timestamp":1776866473958,"version":"3.51.2"},"reference-count":7,"publisher":"American Mathematical Society (AMS)","issue":"317","license":[{"start":{"date-parts":[[2019,9,6]],"date-time":"2019-09-06T00:00:00Z","timestamp":1567728000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["FT160100094"],"award-info":[{"award-number":["FT160100094"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We prove that any prime\n \n \n \n p<\/mml:mi>\n p<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n satisfying\n \n \n \n \n \n \u03d5\n \n <\/mml:mi>\n (<\/mml:mo>\n p<\/mml:mi>\n \n \u2212\n \n <\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n \n \u2264\n \n <\/mml:mo>\n (<\/mml:mo>\n p<\/mml:mi>\n \n \u2212\n \n <\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n \n \/<\/mml:mo>\n <\/mml:mrow>\n 4<\/mml:mn>\n <\/mml:mrow>\n \\phi (p-1)\\leq (p-1)\/4<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n contains two consecutive quadratic non-residues modulo\n \n \n \n p<\/mml:mi>\n p<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n neither of which is a primitive root modulo\n \n \n \n p<\/mml:mi>\n p<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . This improves on results by Luca et al. and Gun et al.\n <\/p>","DOI":"10.1090\/mcom\/3378","type":"journal-article","created":{"date-parts":[[2018,6,6]],"date-time":"2018-06-06T10:19:23Z","timestamp":1528280363000},"page":"1251-1260","source":"Crossref","is-referenced-by-count":5,"title":["Quadratic non-residues that are not primitive roots"],"prefix":"10.1090","volume":"88","author":[{"given":"Tamiru","family":"Jarso","sequence":"first","affiliation":[]},{"given":"Tim","family":"Trudgian","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2018,9,6]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1112\/blms\/bdv018","article-title":"On consecutive primitive elements in a finite field","volume":"47","author":"Cohen, Stephen D.","year":"2015","journal-title":"Bull. Lond. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"issue":"4","key":"2","doi-asserted-by":"publisher","first-page":"325","DOI":"10.4064\/aa129-4-3","article-title":"Distribution of residues modulo \ud835\udc5d","volume":"129","author":"Gun, S.","year":"2007","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"4","key":"3","doi-asserted-by":"crossref","first-page":"387","DOI":"10.21136\/MB.2005.134213","article-title":"Distribution of quadratic non-residues which are not primitive roots","volume":"130","author":"Gun, S.","year":"2005","journal-title":"Math. Bohem.","ISSN":"https:\/\/id.crossref.org\/issn\/0862-7959","issn-type":"print"},{"issue":"1","key":"4","first-page":"97","article-title":"Quadratic non-residues versus primitive roots modulo \ud835\udc5d","volume":"23","author":"Luca, Florian","year":"2008","journal-title":"J. Ramanujan Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0970-1249","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"215","DOI":"10.7169\/facm\/2016.55.2.5","article-title":"Resolving Grosswald\u2019s conjecture on GRH","volume":"55","author":"McGown, Kevin","year":"2016","journal-title":"Funct. Approx. Comment. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0208-6573","issn-type":"print"},{"issue":"4","key":"6","doi-asserted-by":"publisher","first-page":"367","DOI":"10.4064\/aa-42-4-367-389","article-title":"Estimation de la fonction de Tchebychef \ud835\udf03 sur le \ud835\udc58-i\u00e8me nombre premier et grandes valeurs de la fonction \ud835\udf14(\ud835\udc5b) nombre de diviseurs premiers de \ud835\udc5b","volume":"42","author":"Robin, Guy","year":"1983","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"7","first-page":"64","article-title":"Approximate formulas for some functions of prime numbers","volume":"6","author":"Rosser, J. Barkley","year":"1962","journal-title":"Illinois J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0019-2082","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2019-88-317\/S0025-5718-2018-03378-6\/mcom3378_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/www.ams.org\/mcom\/2019-88-317\/S0025-5718-2018-03378-6\/S0025-5718-2018-03378-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2019-88-317\/S0025-5718-2018-03378-6\/S0025-5718-2018-03378-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:03:50Z","timestamp":1776801830000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2019-88-317\/S0025-5718-2018-03378-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,6]]},"references-count":7,"journal-issue":{"issue":"317","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["S0025-5718-2018-03378-6"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3378","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2018,9,6]]}}}