{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:05:50Z","timestamp":1776834350332,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"335","license":[{"start":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000},"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":"<p>\n                    For\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q\">\n                        <mml:semantics>\n                          <mml:mi>q<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">q<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    an odd prime power, we prove that there are always four consecutive primitive elements in the finite field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper F Subscript q\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">F<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {F}_{q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    when\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q greater-than 2401\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>2401<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q&gt; 2401<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/mcom\/3716","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T09:20:41Z","timestamp":1638177641000},"page":"1521-1532","source":"Crossref","is-referenced-by-count":1,"title":["Four consecutive primitive elements in a finite field"],"prefix":"10.1090","volume":"91","author":[{"given":"Tamiru","family":"Jarso","sequence":"first","affiliation":[]},{"given":"Tim","family":"Trudgian","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2021,12,28]]},"reference":[{"key":"1","unstructured":"W. Bosma, J. Cannon, C. Fieker, and A. Steel, The Magma algebra system. I. Version 2.25, January 21, 2020. \\url{http:\/\/magma.maths.usyd.edu.au\/magma\/}."},{"key":"2","unstructured":"A. Brauer, \u00dcber sequenzen von potenzresten, S.-B. Preuss. Akad. Wiss., 1928, 9\u201316."},{"key":"3","first-page":"65","article-title":"Sets of primitive roots","volume":"13","author":"Carlitz, L.","year":"1956","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"189","DOI":"10.2307\/2044741","article-title":"Consecutive primitive roots in a finite field","volume":"93","author":"Cohen, Stephen D.","year":"1985","journal-title":"Proc. Amer. Math. 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Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"973","DOI":"10.2307\/2005534","article-title":"A note on Dirichlet characters","volume":"27","author":"Hudson, Richard H.","year":"1973","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.jnt.2003.06.003","article-title":"On consecutive quadratic non-residues: a conjecture of Issai Schur","volume":"103","author":"Hummel, Patrick","year":"2003","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"key":"10","unstructured":"M. Hunter, The Least Square-free Primitive Root Modulo a Prime, Honours Thesis, ANU, 2016."},{"issue":"317","key":"11","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.1090\/mcom\/3378","article-title":"Quadratic non-residues that are not primitive roots","volume":"88","author":"Jarso, Tamiru","year":"2019","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"12","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"},{"key":"13","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1017\/s0305004100049252","article-title":"Theorems on factorization and primality testing","volume":"76","author":"Pollard, J. 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