{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:56:30Z","timestamp":1776848190997,"version":"3.51.2"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"296","license":[{"start":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T00:00:00Z","timestamp":1459296000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We prove that for all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q greater-than 61\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>61<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q&gt;61<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , every non-zero element 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                    can be written as a linear combination of two primitive roots of\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                    . This resolves a conjecture posed by Cohen and Mullen.\n                  <\/p>","DOI":"10.1090\/mcom\/2950","type":"journal-article","created":{"date-parts":[[2015,3,30]],"date-time":"2015-03-30T10:14:40Z","timestamp":1427710480000},"page":"2979-2986","source":"Crossref","is-referenced-by-count":8,"title":["A proof of the conjecture of Cohen and Mullen on sums of primitive roots"],"prefix":"10.1090","volume":"84","author":[{"given":"Stephen","family":"Cohen","sequence":"first","affiliation":[]},{"given":"Tom\u00e1s","family":"Oliveira e Silva","sequence":"additional","affiliation":[]},{"given":"Tim","family":"Trudgian","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2015,3,30]]},"reference":[{"key":"1","first-page":"189","article-title":"Pairs of primitive elements modulo \ud835\udc5d^{\ud835\udc59}","volume":"26","author":"Chou, Wun Seng","year":"1989","journal-title":"Sichuan Daxue Xuebao","ISSN":"https:\/\/id.crossref.org\/issn\/0490-6756","issn-type":"print"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1112\/S0025579300011050","article-title":"Pairs of primitive roots","volume":"32","author":"Cohen, Stephen D.","year":"1985","journal-title":"Mathematika","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5793","issn-type":"print"},{"key":"3","isbn-type":"print","first-page":"43","article-title":"Primitive elements and polynomials: existence results","author":"Cohen, Stephen D.","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0824788052"},{"issue":"4","key":"4","doi-asserted-by":"publisher","first-page":"299","DOI":"10.4064\/aa143-4-1","article-title":"The strong primitive normal basis theorem","volume":"143","author":"Cohen, Stephen D.","year":"2010","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/BF01810854","article-title":"Primitive elements in finite fields and Costas arrays","volume":"2","author":"Cohen, Stephen D.","year":"1991","journal-title":"Appl. Algebra Engrg. Comm. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0938-1279","issn-type":"print"},{"issue":"1","key":"6","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/0097-3165(84)90015-3","article-title":"Algebraic constructions for Costas arrays","volume":"37","author":"Golomb, Solomon W.","year":"1984","journal-title":"J. Combin. Theory Ser. 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